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When fitting statistical models, some predictors are often found to be correlated with each other, and functioning together. Many group variable selection methods are developed to select the groups of predictors that are closely related to…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic theory is no longer valid. When the dimension is larger than or increasing with the sample…
In the analysis of square contingency tables with ordered categories, it is essential to assess deviations from marginal homogeneity (MH) when marginal equivalency between row and column variables does not hold. Some measures for evaluating…
We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
Sign tests are among the most successful procedures in multivariate nonparametric statistics. In this paper, we consider several testing problems in multivariate analysis, directional statistics and multivariate time series analysis, and we…
An important aspect of modeling spatially-referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the…
The normality assumption for random errors is fundamental in the analysis of variance (ANOVA) models. However, it is rarely subjected to formal testing in practice, and theoretically justified procedures are largely unavailable, especially…
We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function,…
The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
This paper introduces the generalized Hausman test as a novel method for detecting non-normality of the latent variable distribution of unidimensional Item Response Theory (IRT) models for binary data. The test utilizes the pairwise maximum…
We give a review of recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is based on the classic Levene's test for detecting differences in dispersion. It…
Observational studies can play a useful role in assessing the comparative effectiveness of competing treatments. In a clinical trial the randomization of participants to treatment and control groups generally results in well-balanced groups…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…
Many anomaly detection approaches, especially deep learning methods, have been recently developed to identify abnormal image morphology by only employing normal images during training. Unfortunately, many prior anomaly detection methods…