Related papers: Optimal rank-based testing for principal component…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Statistical experiments often seek to identify random variables with the largest population means. This inferential task, known as rank verification, has been well-studied on Gaussian data with equal variances. This work provides the first…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…
Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships,…
We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…
PageRank for Semi-Supervised Learning has shown to leverage data structures and limited tagged examples to yield meaningful classification. Despite successes, classification performance can still be improved, particularly in cases of fuzzy…
In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
In this work, nonparametric log-rank-type statistical tests are introduced in order to verify homogeneity of purely discrete variables subject to arbitrary right-censoring for infinitely many categories. In particular, the Cram\'er-von…
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
In genetic studies of complex diseases, the underlying mode of inheritance is often not known. Thus, the most powerful test or other optimal procedure for one model, e.g. recessive, may be quite inefficient if another model, e.g. dominant,…
We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…
Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be…
Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution-free, are based…