Related papers: Hypothesis Testing for the Covariance Matrix in Hi…

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…

We study the matrix-variate regression problem $Y_i = \sum_{k} \beta_{1k} X_i \beta_{2k}^{\top} + E_i$ for $i=1,2\dots,n$ in the high dimensional regime wherein the response $Y_i$ are matrices whose dimensions $p_{1}\times p_{2}$ outgrow…

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…

Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…

Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…

The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…

Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…

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…

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…

Single-cell RNA-sequencing technologies may provide valuable insights to the understanding of the composition of different cell types and their functions within a tissue. Recent technologies such as spatial transcriptomics, enable the…

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary…

Knockoffs are a popular statistical framework that addresses the challenging problem of conditional variable selection in high-dimensional settings with statistical control. Such statistical control is essential for the reliability of…

A block covariance structure is widely observed across large-scale and high-dimensional datasets in diverse fields such as biology, medicine, engineering, economics, and finance. This pattern entails partitioning a covariance matrix into…

We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical…

Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures…

In this article, we introduce a two-way factor model for a high-dimensional data matrix and study the properties of the maximum likelihood estimation (MLE). The proposed model assumes separable effects of row and column attributes and…

We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the…

We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic…

Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…