Related papers: Inspecting discrepancy between multivariate distri…

Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The…

In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…

We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of…

Binned scatter plots are a powerful statistical tool for empirical work in the social, behavioral, and biomedical sciences. Available methods rely on a quantile-based partitioning estimator of the conditional mean regression function to…

High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…

The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…

The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…

This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…

This paper presents a set of Stata commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution, and a particular type of non-central multivariate t distribution. Specifically, their…

The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…

A comprehensive toolkit is developed for regression analysis of directional data based on a flexible class of angular Gaussian distributions. Informative testing procedures for isotropy and covariate effects on the directional response are…