Nonlinear nonparametric statistics (NNS) algorithm offers new tools for curve fitting. A relationship between k-means clustering and NNS regression points is explored with graphics showing a perfect fit in the limit. The goal of this paper is to demonstrate NNS as a form of unsupervised learning, and supply a proof of its limit condition. The procedural similarity NNS shares with vector quantization is also documented, along with identical outputs for NNS and a k nearest neighbours classification algorithm under a specific NNS setting. Fisher's iris data and artificial data are used. Even though a perfect fit should obviously be reserved for instances of high signal to noise ratios, NNS permits greater flexibility by offering a large spectrum of possible fits from linear to perfect.

There is high confidence that climate change has increased the probability of concurrent temperature-precipitation extremes, changed their spatial-temporal variations, and affected the relationships between drivers of such natural hazards. However, the extent of such changes has been less investigated in Australia. Daily weather data (131 years, 1889-2019) at 700 grid cells (1◦ × 1◦) across Australia was obtained to calculate annual and seasonal mean daily maximum temperature (MMT) and total precipitation (TPR). A nonparametric multivariate copula framework was adopted to estimate the return period of compound hot-dry (CHD) events based on an ‘And’ hazard scenario (hotter than a threshold ‘And’ drier than a threshold). CHD extremes were defined as years with joint return periods of larger than 25 years. Mann-Kendall nonparametric tests was used to analyse trends in MMT and TPR as well as in the frequency of univariate and CHD extremes. A general cooling-wetting trend was observed over 1889-1989. Significant increasing trends were detected over 1990-2019 in the frequency and severity of hot extremes across the country while trends in dry extremes were mostly insignificant (and decreasing). Results showed a significant increase in the association between temperature and precipitation at various temporal scales. The frequency of CHD extremes was mostly stable over 1889-1989, but significantly increased between 1990 and 2019 at 44% of studied grid cells, mostly located in the north, south-east and south-west. Spatial homogeneity (i.e. connectedness) and propagation of extreme events from one grid cell to its neighbouring cells was investigated across Australia. It can be concluded that this connectedness has not significantly changed since 1889.

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.

While the importance of continuous monitoring of electrocardiographic (ECG) or photoplethysmographic (PPG) signals to detect cardiac anomalies is generally accepted in preventative medicine, there remain major barriers to its actual widespread adoption. Most notably, current approaches tend to lack real-time capability, exhibit high computational cost, and be based on restrictive modeling assumptions or require large amounts of training data. We propose a lightweight and model-free approach for the online detection of cardiac anomalies such as ectopic beats in ECG or PPG signals based on the change detection capabilities of Singular Spectrum Analysis (SSA) and nonparametric rank-based cumulative sum (CUSUM) control charts. The procedure is able to quickly detect anomalies without requiring the identification of fiducial points such as R-peaks and is computationally significantly less demanding than previously proposed SSA-based approaches. Therefore, the proposed procedure is equally well suited for standalone use and as an add-on to complement existing (e.g. heart rate (HR) estimation) procedures.

Clinical agreement between two quantitative measurements on a group of subjects is generally assessed with the help of the Bland-Altman (B-A) limits. The interpretation regarding agreement is based on whether B-A limits are within the pre-specified clinical tolerance. Thus, clinical tolerance limits are necessary for this method. We argue in this communication that such limits of clinical tolerance can be directly used for assessing agreement and plead that this nonparametric approach is simple and robust to the distribution pattern and outliers. Such direct use of clinical tolerance limits has more flexibility, and it is more effective in assessing the extent of agreement.

This paper studies the contemporaneous relationship between S&P 500 index returns and log-increments of the market volatility index (VIX) via a nonparametric copula method. Specifically, we propose a conditional dependence index to investigate how the dependence between the two series varies across different segments of the market return distribution. We find that: (a) the two series exhibit strong, negative, extreme tail dependence; (b) the negative dependence is stronger in extreme bearish markets than in extreme bullish markets; (c) the dependence gradually weakens as the market return moves toward the center of its distribution, or in quiet markets. The unique dependence structure supports the VIX as a barometer of markets' mood in general. Moreover, applying the proposed method to the S&P 500 returns and the implied variance (VIX²), we find that the nonparametric leverage effect is much stronger than the nonparametric volatility feedback effect, although, in general, both effects are weaker than the dependence relation between the market returns and the log-increments of the VIX.

In this paper we describe a nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions. Given $N$ independent observations, convexity theory shows that the NPML estimator is discrete with at most $N$ support points. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. The probability of the support points is found by a Primal-Dual Interior-Point method; the location of the support points is found by an Adaptive Grid method. Our method is able to handle high-dimensional and complex multivariate mixture models.An important application is discussed for the problem of population pharmacokinetics and a non-trivial example is treated.Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics.

Statistical modeling lies at the heart of product design and development throughout numerous engineering disciplines, especially since processing large amounts of data has become increasingly ubiquitous. While mathematical statistics provide elegant guidance pertaining to the question of whether or not some particular underlying modeling assumptions are justified and appropriate, when pursuing a more comprehensive assessment of product design and development other considerations often increase in significance. Therefore, we will examine and analyze the tedious interactions and implications of statistical modeling choices and product liability exposure. To the best of our knowledge, this paper is the first to draw attention to and explore some often overlooked or oversimplified dangers and pitfalls that enter the equation when product design heavily relies on statistical modeling. In particular, through a diligent analysis of both statistical and legal aspects we will explore how statistically optimal procedures may yield far from optimal outcomes in terms of product liability when applied to actual real life problems and why suboptimal nonparametric or robust approaches may constitute better alternatives.

Genomic selection (GS) can accelerate variety improvement when training set (TS) size, and its relationship with the breeding set (BS) are optimized for prediction accuracies (PA) of genomic prediction (GP) models. Sixteen GP algorithms were run on phenotypic best linear unbiased predictors (BLUPs) and estimators (BLUEs) of resistance to both fall armyworm (FAW) and maize weevil (MW) in a tropical maize panel. For MW resistance, 37% of the panel was the TS, and BS was the remainder whilst for FAW, random-based training sets (RBTS) and pedigree-based training sets (PBTS) were designed. PAs achieved with BLUPs varied from 0.66 to 0.82 for MW resistance traits, and, for FAW resistance, 0.694 to 0.714 for RBTS of 37%, and 0.843 to 0.844 for RBTS of 85%, and, these were at least two-fold those from BLUEs. For PBTS, FAW resistance PAs were generally higher than those for RBTS, except for one dataset. GP models generally showed similar PAs across individual traits whilst the TS designation was determinant since a positive correlation (R=0.92***) between TS size and PAs was observed for RBTS and, for the PBTS, it was negative (R=0.44**). This study pioneers the use of GS for maize resistance to insect pests in sub-Saharan Africa.

Nowadays, according to spectacular improvement in health care and biomedical level, a tremendous amount of data is recorded by hospitals. In addition, the most effective approach to reduce disease mortality is to diagnose it as soon as possible. As a result, data mining by applying machine learning in the field of diseases provides good opportunities to examine the hidden patterns of this collection. An exact forecast of the mortality after heart surgery will cause Successful medical treatment and fewer costs. This research wants to recommend a new stacking predictive model after utilizing the random forest feature importance method to foresee the mortality after heart surgery on a highly unbalanced dataset by using the most practical features. To solve the unbalanced data problem, a combination of the SVM-SMOTE over-sampling algorithm and the Edited-Nearest-Neighbor under-sampling algorithm is used. This research compares the introduced model with some other machine learning classifiers to ensure efficiency through shuffle hold-out and 10-fold cross-validation strategies. In order to validate the performance of the implemented machine learning methods in this research, both shuffle hold-out, and 10-fold cross-validation results indicated that our model had the highest efficiency compared to the other models. Furthermore, the Friedman statistical test is applied to survey the differences between models. The result demonstrates that the introduced stacking model reached the most accurate predicting performance after Logistic Regression.