Related papers: Hotelling's test for highly correlated data
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 the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling's classical $T^2$ test does not work for this "large $p$, small $n$" situation. The proposed test…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
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…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
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…
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or…
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…
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…
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…
We discuss a one-sample location test that can be used in the case of high-dimensional data. For high-dimensional data, the power of Hotelling's test decrises when the dimension is close to the sample size. To address this loss of power,…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
We adapt Higher Criticism (HC) to the comparison of two frequency tables which may -- or may not -- exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis…
We propose a method of testing the shift between mean vectors of two multivariate Gaussian random variables in a high-dimensional setting incorporating the possible dependency and allowing $p > n$. This method is a combination of two…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
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…
Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…
The standard methods for detecting differential gene expression are mostly designed for analyzing a single gene expression experiment. When data from multiple related gene expression studies are available, separately analyzing each study is…
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be…