This paper compares the finite sample performance of three non-parametric threshold estimators via Monte Carlo method. Our results show that the finite sample performance of the three estimators is not robust to the relative position of the threshold level along the distribution of threshold variable, especially when a structural change occurs at the tail part of the distribution.

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested by generalizing the uniform shrinkage of ridge regression to the non-uniform shrinkage, which was shown to perform well under sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (the first version published on 2023-12-07 at https://cran.r-project.org/package=g.ridge) that implements both the ridge estimator and generalized ridge estimators. The package equips with the generalized cross-validation for automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with the normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on “glmnet”, and hence, it can be the most recommended estimator under sparse and high-dimensional models. We demonstrate the package using the intracerebral hemorrhage data.

In this paper a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered and the robustness is studied on the basis of a simulation study. Previously, the composite minimum density power divergence estimator is introduced and its asymptotic properties are studied.

Dry periods and drought are inherent natural occurrences. However, due to the increasing pressures of global warming and climate change, these events become more frequent and severe on a global scale. These phenomena can be traced with various indicators and related indices proposed by various scholars. In general, drought risk assessment is done by modelling these indicators and determining the drought occurrence probabilities. The proposed adaptation introduces the "Kaplan-Meier Estimator," a non-parametric statistic traditionally used in medical contexts to estimate survival functions from lifetime data. The study aims to repurpose this methodology to assess drought risk by treating past droughts as "events" and evaluating the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) and map these results for a better understanding of the drought risks within larger spatial scales such as a river basin. The adapted method provides the probability of non-occurrence, with inverted results indicating the likelihood of drought occurrence. As a case study, the method is applied to SPI and SPEI values at different time steps (3, 6, and 12 months) across 27 meteorological stations in the Gediz River Basin, located in Western Turkey—a region anticipated to be profoundly affected by global climate change. The results are represented as the generated drought risk maps and curves, which indicate that (i) drought risks increase as the considered period extends, (ii) drought risks decrease as the utilized indicator timescales increase, (iii) locally plotted drought curves indicate higher drought risks as their initial slope get steeper. The method used enables the generation of historical evidence based spatially distributed drought risk maps which expose more vulnerable areas within the river basin.

In this paper, we will use the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength ℜ=P[X>Y] based on independent adaptive progressive censored samples that were taken from the Chen distributions. An approximate confidence interval of ℜ is constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. The Bayesian estimation of ℜ is obtained based on the balanced loss function, which comes in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating ℜ using the Bayesian approach, all the unknown parameters of the Chen distributions are assumed to be independently distributed and to have informative gamma priors. Further, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm is used to compute the Bayes estimate of ℜ and the associated highest posterior density credible interval. In the end, simulation research are used to assess the general overall performance of the proposed estimators and a real data set is provided to exemplify the theoretical results.

Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge either successively or in close succession. The trivariate distribution can demonstrate the risk of the compound phenomenon more realistically rather than considering each contributing factor independently or in a pairwise dependency. Recently vine copula has been recognized as the highly flexible approach to constructing a higher dimensional joint density framework. In such construction, parametric class copula with parametric univariate marginal distributions is often involved. Such incorporation can lack flexibility due to parametric functions with prior distribution assumptions about their univariate marginal and/or copula joint density. This study introduces the vine copula approach in a nonparametric setting by introducing Bernstein and Beta kernel copula density in establishing trivariate flood dependence. The proposed model is applied to 46 years of flood characteristics collected on the west coast of Canada. The univariate flood marginal distribution is modelled using nonparametric kernel density estimation (KDE). The 2-D Bernstein estimator and Beta kernel copulas estimator are tested independently in capturing pairwise dependencies to establish D-vine structure in a stage-wise nesting approach in three alternative ways, each by permutating the location of the conditioning variable. The best-fitted vine structure is selected using goodness-of-fit (GOF) test statistics. The performance of the nonparametric vine approach is also compared with the vine constructed in the parametric and semiparametric fitting procedure. Investigation reveals that the D-vine constructed using Bernstein copula with normal KDE marginals nonparametrically performed well in capturing dependence of the compound events. Finally, the derived nonparametric model is used in the estimation of trivariate OR- and AND-joint return periods, further employed in estimating failure probability (FP) statistics. The trivariate return periods for the AND-joint case are higher than for the OR-joint case for the same flood combination. Also, the trivariate flood hazard results in a high-value FP than bivariate and univariate events. Ignoring the trivariate dependence could result in the underestimation of FP

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve their fit. In this paper, we explore a further extension of the quasi-Lindley model. Maximum likelihood, least square error, Anderson-Darling algorithm, and expectation-maximization algorithm are four techniques for estimating the parameters under study. All techniques provide accurate and reliable estimates of the parameters. However, the mean square error of the expectation maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a dynamical systems data set, and the analysis shows that it outperforms the other models in all statistical models considered.

The negative binomial regression model (NBRM) is a generalized linear model which relaxes the restrictive assumption by the Poisson regression model when the variance is equal to the mean. The estimation of the parameters of the NBRM is obtained using the maximum likelihood (ML) method. Maximum likelihood estimator becomes unstable when the explanatory variables are linearly dependent, a situation known as multicollinearity. Based on this, we developed a new estimator called modified jackknifed Negative Binomial Kibria-Lukman (MJNBKL) estimator for the radiation of multicollinearity in NBRM using four different biasing (shrinkage) parameters. We establish superiority condition for MJNBKL estimator over the ones. The performance MJNBKL estimator was ascertained by comparing it with the existing ones through a Monte Carlo simulation study and two real life application datasets. The results of the simulation and real life application show that MJNBKL estimator outperformed the other estimators compared with by having the smallest MSE across all sample sizes and for different levels of correlation for the four biasing parameters used and the third biasing parameter is the optimal shrinkage parameter with the lowest MSE.

Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection regression depth (PRD) represent the two most promising notions in regression. Carrizosa depth DC is another depth notion in regression. Depth induced regression medians (maximum depth estimators) serve as robust alternatives to the classical least squares estimator. The uniqueness of regression medians is indispensable in the discussion of their properties and the asymptotics (consistency and limiting distribution) of sample regression medians. Are the regression medians induced from RD, PRD, and DC unique? Answering this question is the main goal of this article. It is found that only the regression median induced from PRD possesses the desired uniqueness property. The conventional remedy measure for non-uniqueness, taking average of all medians, might yield an estimator that no longer possesses the maximum depth in both RD and DC cases. These and other findings indicate that the PRD and its induced median are highly favorable among their leading competitors.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

Spatial regression models have garnered significant attention across several disciplines, including functional magnetic resonance imaging analysis, econometrics, home price analysis, and many other domains. The phenomenon of sparsity is often found in nature, when a limited number of factors contribute significantly to the overall variation. Spatial regression models frequently use sparsity to indicate less complex computational and more superficial covariance structures. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach for estimating the vector of regression coefficients in the spatial error model, taking into consideration of the prior knowledge that some coefficients are insignificant and there is multicollinearity among the regressors. It also introduces pretest and shrinkage ridge estimators for spatial error regression models, evaluating their performance compared to traditional maximum likelihood estimators. It also assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes.

Vibrations of blades and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to design a controller which it utilizes a minimum-variance unbiased estimator(MVUE) to estimate both state and unknown input. The stability analysis proved that the proposed SDAC is bounded in mean square.In order to verify the performance of the minimum-variance unbiased estimator and the proposed SDAC, numerical simulations using Matlab/Simulink have been carried out for the National Renewable Energy Laboratory 5-MW wind turbine.Under the different circumstance which exists the random process and measure noise and noise free. It is shown that the estimation value by MVUE can tracking the real state and unknown input. The results are also compared to the traditional linear quadratic regulator(LQR) and show that the proposed stochastic disturbance accommodating control scheme can further reduce displacement in edgewise vibrations direction and the control strategy is more effective than the LQR.

In this paper a more flexible extension of the Fréchet distribution is introduced. The new distribution is defined by means of the stochastic representation as the quotient of two independent random variables, a Fréchet distribution and the power of a random variable with uniform distribution in the interval (0,1). We will call this new extension the Slash Fréchet distribution and one of its main characteristics is that its tails are heavier than the Fréchet distribution. The general density of this distribution and some basic properties are determined. Its moments, skewness coefficients and kurtosis are calculated. In addition, the estimation of the model parameters is obtained by the method of moments and maximum likelihood. Finally, two applications with real data are performed by fitting the new model and comparing it with the Fréchet distribution.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh Weibull (RW) distribution based on progres-sive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley and Tierney-Kadane's approximation method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes esti-mates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Real lifetime data sets belonging to the cancer types as bladder cancer, head and neck cancer, and leukemia are used to illustrate the emprical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.

The proton exchange membrane fuel cell (PEMFC) is a critical and essential component of zero-emission electro-hydrogen generators. An accurate prediction of its performance is important for optimal operation management and preventive maintenance of these generators. However, the prediction is not simple because the PEMFCs have complex electrochemical reactions with multiple nonlinear relations between operating variables as inputs and voltage as output. In this paper, we propose an efficient prediction approach based on XGBRegressor and Tree-structured Parzen Estimator. In addition, to better select relevant features, Kernel Principal Component Analysis and Mutual Information are jointly used. The proposed approach allows consideration of the dynamic operating conditions of the PEMFC. To test and validate the robustness of the proposed approach, a real data-set of ten PEMFCs was considered. Furthermore, a comparison study with traditional machine learning models, such as artificial neural networks and support vector machine regression, was investigated. The obtained results confirm that our model outperforms the considered traditionel machine learning models.

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in the small-sized sample or highly heterogeneous assemblage. Estimating species richness in a large-scale region typically involves an integrated data set consisting of subsamples collected independently from different subregions. However, the pooled sample of integrated data is no longer a random sample from the entire region, and the use of different sampling schemes results in variations in data formats. Consequently, employing a single sampling distribution to model the pooled sample becomes impractical, rendering existing richness estimators inadequate. This study theoretically explains the applicability of Chao's lower bound estimators in estimating species richness for large-scale areas using the pooled sample. Additionally, a new nonparametric estimator is introduced, which adjusts the bias of Chao's lower bound estimator by leveraging the Good-Turing frequency formula. This proposed estimator only utilizes the pooled sample's singleton, doubleton, and tripleton richness. Simulated data sets across various models are employed to demonstrate the statistical performance of the estimator, showcasing its ability to reduce bias and provide accurate 95% confidence intervals. Real data sets are also utilized to illustrate the practical application of the proposed approach.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

In the case of long-stator linear drive, unlike rotative drives for which speed or position sensors are a single unit attached to the shaft, these sensors extend along the guideway. The position signals transmitted from maglev vehicle can’t meet the need of the real-time propulsion control in the on-ground inverter power substations. In this paper the design of the propulsion inverter control system with a position estimator for driving long-stator synchronous motor in high speed maglev train is proposed. The experiments have been carried out at the 150m long guideway in O-song test track. To investigate the performance of the position estimator, the propulsion control system with and without the position estimator are compared. The result confirms that the proposed strategy can meet the dynamic property need of propulsion inverter control system for driving long-stator linear synchronous motors

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

This study investigates the trend in monthly and annual rainfall, minimum and maximum temperature (T_min and T_max) using the Mann–Kendall (MK) test and Sen’s slope (SS) method and evaluates the significance of their variability for maize, sorghum and millet yields in northern Togo employing multiple regression analysis. The historical data of Kara, Niamtougou, Mango and Dapaong weather stations from 1977 to 2012 were used. Four non-parametric methods—Alexandersson’s Standard Normal Homogeneity Test (SNHT), Buishand’s Range Test (BRT), Pettitt’s Test (PT) and Von Neumann’s Ratio Test (VNRT)—were applied to detect homogeneity in the data. For the data which were serially correlated, a modified version of the MK test (pre-whitening) was utilised. Results showed an increasing trend in the annual rainfall in all four locations. However, this trend was only significant at Dapaong (p < 0.1). There was an increasing trend in T_max at Kara, Mango and Niamtougou, unlike Dapaong where T_max revealed a significant decreasing trend (p < 0.01). Similarly, there was an increasing trend in T_min at Kara, Mango and Dapaong, unlike Niamtougou where T_min showed a non-significant decreasing trend (p > 0.05). Rainfall in Dapaong was found to have increased (7.79 mm/year) more than the other locations such as Kara (2.20 mm/year), Niamtougou (4.57 mm/year) and Mango (0.67 mm). T_max increased by 0.13, 0.13 and 0.32 °C per decade at Kara, Niamtougou and Mango, respectively, and decreased by 0.20 per decade in Dapaong. Likewise, T_min increased by 0.07, 0.20 and 0.02 °C per decade at Kara, Mango and Dapaong, respectively, and decreased by 0.01 °C per decade at Niamtougou. Results of multiple regression analysis revealed nonlinear yield responses to changes in rainfall and temperature. Rainfall and temperature variability affects rainfed cereal crops production, but the effects vary across crops. The temperature has a positive effect on maize yield in Kara, Niamtougou and Mango but a negative effect on sorghum in Niamtougou and millet in Dapaong, while rainfall has a negative effect on maize yield in Niamtougou and Dapaong and millet yield in Mango. In all locations, rainfall and temperature variability has a significant effect on the cereal crop yields. There is, therefore, a need to adopt some adaptation strategies for sustainable agricultural production in northern Togo.

In the full load operating range, wind turbines typically use pitch control to maintain rotor speed and output power at their rated values to guarantee the whole system’s safety. Blade pitch actuators are subject to physical limitations and safety requirements, which imposes strict constraints on pitch angle’s amplitude and rate of change. These constraints will bring windup problem to the integral part of the pitch controller. It leads to deterioration of the pitch control system’s performance or even the instability problem, especially for large-scale turbines operating in extreme uncertain wind conditions or suffering from cyber attacks. This paper designs an anti-windup robust pitch angle control strategy to deal with pitch rate constraint issue to enhance the security of control system. First, to facilitate controller design, a filtered tracking error technique is employed to transform the nonaffine form into an affine one. Subsequently, a feedback robust controller based on UDE is developed to handle the model’s uncertainty and external disturbances. To address the issue of integral saturation in the pitch system and guarantee its safety, an elliptical bounded constraint is integrated into the designed UDE strategy. This bounded UDE controller can improve the stability of power generation quality, reduces the mechanical loads on components and enhance the whole system’s safety. Finally, the effectiveness of the proposed scheme is verified on the Wind Turbine Blockset platform in Matlab/Simulink. It can achieve better performance than the traditional method.

Droughts are among the major natural hazards that are spreading to many parts of the world with huge multi-dimensional impacts. For Continental Croatia an extensive analysis of drought phenomenon is presented based on meteorological E-OBS gridded dataset (0.25° x 0.25°), within the period of 1950 to 2022. The drought events were characterized by the Standardized Precipita-tion Evapotranspiration Index (SPEI) applied to different time-scales (6 and 12 months) in order to describe the subannual and annual variability of drought. The spatiotemporal patterns of drought are obtained through principal component analysis (PCA) and K-means clustering (KMC) applied to the SPEI field. An areal drought evolution analysis and the changes in the frequency of occur-rence of the periods under drought conditions were achieved by using a kernel occurrence rate es-timator (KORE). The Modified Mann-Kendall (MMK) test coupled with the Sen’s slope estimator test are applied to the SPEI series in order to quantify the drought trends throughout the country. According to drought events history and considering the different morphoclimatic characteristics of the study area the results showed that Croatia could be divided into three different and spatial-ly well-defined regions with specific temporal and spatial characteristics of droughts (Central North, Eastern and Southern regions). It is shown that there is a manifest increase in the percent-age of area affected by drought as well as in the yearly drought occurrences rates in both Central North and Eastern regions and an evident decrease in the Southern region for both 6 and 12 month SPEI time-scales. In the observation of the drought temporal characteristics, it was found that downward trends expressing increasing drought severities were strongly significant in North and Eastern regions while a few significant upward trends were seen in Southern region. From this study, it is possible to obtain a broader view of the historical behaviour of droughts in Croatia with results providing useful support for drought risk assessment and decision-making processes.

The study focused on two climatic variables i.e. precipitation and stream flow for analysing change in trend of rainfall for the River Ssezibwa Catchment area and stream flow of River Ssezibwa. This Catchment is found in the districts of Mukono and Buikwe in Uganda. In this area agriculture is majorly dependent on rainfall and irrigation on a small scale. However, rainfall occurrence has become unpredictable over the past few years as result of the changes in patterns of weather. This has caused severe effects on the agricultural cropping system as well as caused negative effects on the natural water resources. Stream flow data of 57 years (1960 – 2017) and rainfall data for 35 years (1982 – 2017) on a daily basis was analysed to find out the trend and detect change point. Trend analysis was done by using the non-parametric analysis while the change point detection was carried out by using the Pettit test (1979).Magnitude of trend for the time series data was carried out using Sen’s Slope estimator and Mann – Kendall test was done to determine the trend. Results from the statistical analysis highlighted that; for stream flow the trend was generally positive and change point detected to be in the year 2000 while for rainfall data analysis indicated that the trend was predominantly negative and change point was in the year 1998.

Soybean with insignificant differences in appearance have large differences in their internal physical and chemical components, therefore follow-up storage, transportation and processing require targeted differential treatment. A fast and effective machine learning method based on hyperspectral data of soybean for pattern recognition of categories is designed as a non-destructive testing method in this paper. A hyperspectral-image dataset with 2299 soybean seeds in 4 categories is collected; Ten features is selected by extreme gradient boosting algorithm from 203 hyperspectral bands in range 400 to 1000 nm; A Gaussian radial basis kernel function support vector machine with optimization by the Tree-structured Parzen Estimator algorithm is built as TPE-RBF-SVM model for pattern recognition of soybean categories. The metrics of TPE-RBF-SVM are significantly improved compared with other machine learning algorithms. The accuracy is 0.9165 in the independent test dataset which is 9.786% higher for vanilla RBF-SVM model and 10.02% higher than the extreme gradient boosting model.

The work consisted in identifying possible effects from heavy metals (HMs) pollution due to waste disposal activities in three potentially polluted sites located in Basilicata (Italy), where a release of pollutants with values over the thresholds allowed by the Italian legislation was detected. The potential variations in the physiological efficiency of vegetation have been analyzed through the multitemporal processing of satellite images. In detail, Landsat 5 Thematic Mapper (TM) and Landsat 8 Operational Land Imager (OLI) images were used to calculate the Normalized Difference Vegetation Index (NDVI) trend over the years. Then, the multitemporal trends were analyzed using the median of Theil-Sen, a non-parametric estimator particularly suitable for the treatment of remote sensing data, being able to minimize the outlier effects due to exogenous factors. Finally, the subsequent application of the Mann-Kendall test on the trends identified by Theil-Sen slope allowed the evaluation of trends significance and, therefore, the areas characterized by the effects of contamination on vegetation. The application of the procedure to the three survey sites led to the exclusion of the presence of significant effects of HMs contamination on the vegetation surrounding the sites during the years of waste disposal activities.

Reverse-order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse-order laws for a matrix product AB is (AB)^(i,...,j) = B^(i,...,j)A^(i,...,j), where (·)^i,...,j denotes an {i,...,j}-generalized inverse of matrix. Because {i,...,j}-generalized inverse of a general matrix is not necessarily unique, the relationships between both sides of the reverse-order law can be divided into four situations for consideration. In this article, we first introduce a linear mixed model y = ABβ + Aγ + ε, present two least-squares methodologies to estimate the fixed parameter vector  in the model, and describe the connections between the two least-squares estimators and the reverse-order laws for generalized inverses of the matrix product AB. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of B^(i,...,j)A^(i,...,j), as well as necessary and sufficient conditions for B^(i,...,j)A^(i,...,j) to be invariant with respect to the choice of A^(i,...,j) and B^(i,...,j). We then present a unied approach to the 512 set inclusion problems {(AB)^(i,...,j) ⊇ {B^(i,...,j)A^(i,...,j)}for the eight commonly-used types of generalized inverses of A, B, and AB using the block matrix representation method (BMRM), matrix equation method (MEM), and matrix rank method (MRM), where {(·)^(i,...,j)} denotes the collection of all {i,...,j}-generalized inverse of a matrix.

In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the Variational Quantum Classifier (VQC) and the Quantum Kernel Estimator (QKE). We evaluate the performance of these classifiers on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, we developed a data set based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results.\\ Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers like XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes.\\ Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field.\\ To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.

Rainfall variability has resulted in extreme events like devastating floods and droughts which is the main cause of human vulnerability to precipitation in West Africa. Attempts have been made by previous studies to understand rainfall variability over Ghana but these have mostly focused on the major rainy season of April-July, leaving a gap in our understanding of the variability in the September-November season which is a very important aspect of the Ghanaian climate system. The current study seeks to close this knowledge gap by employing statistical tools to quantify variabilities in rainfall amounts, rain days, and extreme precipitation indices in the minor rainfall season over Ghana. We find extremely high variability in rainfall with a Coefficient of variation (CV) between 25.3% and 70.8%, and moderate to high variability in rain days (CV=14.0% - 48.8%). Rainfall amount was found to be higher over the middle sector (262.7 mm – 400.2 mm) but lowest over the east coast (125.2 mm – 181.8 mm). Analysis of the second rainfall season using the Mankandell Test presents a non-significant trend of rainfall amount and extreme indices (R10, R20, R99p, and R99p) for many places in southern Ghana. Rainfall Anomaly Indices show that the middle sector recorded above normal precipitation which is the opposite for areas in the transition zone. The result of this work provides a good understanding of rainfall in the minor rainfall season and may be used for planning purposes.

Cryptocurrencies have obtained a crucial position in the international financial landscape. The cryptocurrency market has been perceived as a highly volatile market since the inception of Bitcoin. This study investigates the relevant performance of extreme value models (EVM) in estimating the Value-at-Risk (VaR) of Bitcoin and Ethereum returns. The extreme value mixture models, GPD-Normal-GPD (GNG) and GPD-KDE-GPD models are fitted to the returns of Bitcoin and Ethereum and the Kupiec likelihood backtesting procedure is performed on the VaR estimates to assess the fits. Both models’ results showed that the fits were a much more decent representation of the observed data when compared to the Normal distribution. The backtesting results showed that the GPD-KDE-GPD model’s fit was superior to that of the GPD-Normal-GPD for both sets of returns at all VaR risk levels except at the 99% level. The results of this study may assist with understanding the dynamics and risks associated with cryptocurrencies and can serve as a beneficial tool for decision-making and risk management to investors, traders, financial institutions and many other participants in the cryptocurrency ecosystem.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.