The testing of high-dimensional normality has been an important issue and has been intensively studied in literatures, it depends on the Variance-Covariance matrix of the sample, numerous methods have been proposed to reduce the complex of the Variance-Covariance matrix. The principle component analysis(PCA) was widely used since it can project the high-dimensional data into lower dimensional orthogonal space, and the normality of the reduced data can be evaluated by Jarque-Bera(JB) statistic on each principle direction. We propose two combined statistics, the summation and the maximum of one-way JB statistics, upon the independency of each principle direction, to test the multivariate normality of data in high dimensions. The performance of the proposed methods is illustrated by the empirical power of the simulated data of normal data and non-normal data. Two real examples show the validity of our proposed methods.

Random Forest (RF) is a widely used data prediction and variable selection technique. However, the variable selection aspect of RF can become unreliable when there are more irrelevant variables than relevant ones. In response, we introduced the Bayesian Random Forest (BRF) method specifically designed for high-dimensional datasets with a sparse covariate structure. Our research demonstrates that BRF possesses the oracle property, which means it achieves strong selection consistency without compromising efficiency or bias.

In this work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

Agile methods promise to achieve high productivity and provide high-quality software. Agile software development is the most important approach that has spread through the world of software development over the past decade. Software team productivity measurement is essential in agile teams to increase the performance of software development. Due to the prevalence of agile methodologies and increasing competition of software development companies, software team productivity has become one of the crucial challenges for agile software companies and teams. Awareness of the level of team productivity can help them to achieve better estimation results on the time and cost of the projects. However, to measure software productivity, there is no definitive solution or approach whether in traditional and agile software development teams that lead to the occurrence of many problems in achieving a reliable definition of software productivity. Hence, this study aims to propose a statistical model to assess the team’s productivity in agile teams. A survey was conducted with forty software companies and measured the impact of six factors of the team on productivity in these companies. The results show that team effectiveness factors including inter-team relationship, quality conformance by the team, team vision, team leader, and requirements handled by the team had a significant impact on the team’s productivity. Moreover, the results also state that inter-team relations affect the most on software teams’ productivity. Finally, the model fit test showed that 80% of productivity depends on team effectiveness factors.

Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search.

The objective of this study is to examine a nonparametric estimate , using the kernel approach, of the conditional distribution function of a scalar response variable that is given a random variable whose values take place in a separable real Hilbert space. The observations will be dependent on one another in a quasi-associated fashion. The pointwise practically perfect consistencies with rates of this estimator are established by us under some broad conditions. The study’s major objective is to investigate the convergence rate of the proposed estimator and its application in the convergence rate and asymptotic normality of the hazard function. The asymptotic normality of the developed estimator is established precisely. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data.

Oscillometric blood pressure (BP) devices currently estimate a single point but do not identify fluctuations in BP or distinguish them from variations in response to physiological properties. In this paper, to analyze BP normality based on oscillometric measurements, we use statistical approaches including kurtosis, skewness, Kolmogorov-Smirnov, and correlation tests. Then, to mitigate uncertainties, we use a deep neural network (DNN) to determine the confidence limits (CLs) of BP measurements based on their normality. The proposed DNN regression model decreases the standard deviation of error (SDE) of the mean error (ME) and the mean absolute error (MAE) and reduces the uncertainty of the CLs and SDEs of the proposed technique. We validate the normality of the distribution of the BP estimation distribution which fits the Gaussian distribution very well. We use a rank test in the DNN regression model to demonstrate the independence of the artificial SBP and DBP estimations. First, we perform statistical tests to verify the normality of the BP measurements for individual subjects. The proposed methodology provides accurate BP estimations and reduces the uncertainties associated with the CLs and SDEs based on the DNN regression estimator.

The aim of this paper is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random. The estimators are constructed by the kernel method, and some asymptotic properties such as probability convergence rates of the nonparametric component and asymptotic distribution of the parametric and nonparametric components are established under certain conditions. Next, the performances and the superiority of these estimators are presented and examined using a study on simulated data and on real data by carrying out a comparison between our semi-functional partially linear model with MAR estimator (SFPLRM), the semi-functional partially linear model with the full-case estimator (SFPLRC) and the nonparametric functional model estimator with MAR (FNPM). The results show that the proposed estimators outperform existing estimators as the number of random missing data increases.