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This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we…
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…
Due to rapid technological advances, a wide range of different measurements can be obtained from a given biological sample including single nucleotide polymorphisms, copy number variation, gene expression levels, DNA methylation and…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
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…
For the mean vector test in high dimension, Ayyala et al.(2017,153:136-155) proposed new test statistics when the observational vectors are M dependent. Under certain conditions, the test statistics for one-same and two-sample cases were…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
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…
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…
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…
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…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
The generalized direction detection (GDD) problem involves determining the presence of a signal of interest within matrix-valued data, where the row and column spaces of the signal (if present) are known, but the speciffc coordinates are…
Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…
In many clinical trials, individuals in different subgroups have experience differential treatment effects. This leads to individualized differences in treatment benefit. In this article, we introduce the general concept of predictive…
A major task in genetic studies is to identify genes related to human diseases and traits to understand functional characteristics of genetic mutations and enhance patient diagnosis. Besides marginal analyses of individual genes,…
We introduce a unified approach to testing a variety of rather general null hypotheses that can be formulated in terms of covariances matrices. These include as special cases, for example, testing for equal variances, equal traces, or for…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…