Related papers: An Improvement on the Hotelling $T^2$ Test Using t…
Many tests have been proposed to remedy the classical Hotelling's $T^2$ test in the "large $p$, small $n$" paradigm, but the existence of an optimal sum-of-squares type test has not been explored. This paper shows that under certain…
For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the…
We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's $T^2$. To choose the regularization parameter, a method is derived that aims at maximizing…
This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…
Designed gene expression micro-array experiments, consisting of several treatment levels with a number of replicates per level, are analyzed by applying simple tests for group differences at the per gene level. The gene level statistics are…
This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine…
Hotelling's $T^2$-test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and…
In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower…
Hotelling's T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the…
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on…
In paired design studies, it is common to have multiple measurements taken for the same set of subjects under different conditions. In observational studies, it is many times of interest to conduct pair matching on multiple covariates…
This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov…
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…
Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…
We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance under a finite symmetry group selected from a candidate…
It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target.…
A Cramer moderate deviation theorem for Hotelling's $T^2$-statistic is proved under a finite $(3+\delta)$th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as…
Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…