Related papers: Multi-level Thresholding Test for High Dimensional…

We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each group and sharing information about the space…

There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more…

This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to…

Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock…

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…

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

This paper explores a variety of topics related to the question of testing the equality of covariance matrices in multivariate linear models, particularly in the MANOVA setting. The main focus is on graphical methods that can be used to…

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…

Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…

How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…

In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…