Related papers: High-Dimensional Invariant Tests of Multivariate N…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard $d$-variate normal distribution as the unique solution of an initial value problem of…
Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based…
In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the…
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…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…
Regression discontinuity (RD) designs with multiple running variables arise in a growing number of empirical applications, including geographic boundaries and multi-score assignment rules. Although recent methodological work has extended…
Multi-collinearity is a wide-spread phenomenon in modern statistical applications and when ignored, can negatively impact model selection and statistical inference. Classic tools and measures that were developed for "$n>p$" data are not…
Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many…
Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…
We propose new affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution. The test statistics are obtained using canonical correlations between sets of sample…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
The objective of the paper is to study accuracy of multi-class classification in high-dimensional setting, where the number of classes is also large ("large $L$, large $p$, small $n$" model). While this problem arises in many practical…