Related papers: A New Two-Sample Test for Covariance Matrices in H…
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
We consider estimation of high-dimensional long-run covariance matrices for time series with nonconstant means, a setting in which conventional estimators can be severely biased. To address this difficulty, we propose a difference-based…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When a theoretical model for the covariance matrix…
Power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics in recent years. Existing tests possess their respective high-power regions, and we may lack prior knowledge about the…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
In this paper, we propose a new test for the equality of several covariance functions for functional data. Its test statistic is taken as the supremum value of the sum of the squared differences between the estimated individual covariance…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…