Related papers: Optimal rank-based testing for principal component…
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
The primary analysis for longitudinal randomized controlled trials (RCTs) often compares treatment groups at the last timepoint, referred to as the landmark time. Assuming data are normally distributed and missing at random, the mixed model…
In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…
Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…
Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
In this article, we develop a test for multivariate location parameter in elliptical model based on the forward search estimator for a specified scatter matrix. Here, we study the asymptotic power of the test under contiguous alternatives…
The development of high-dimensional white noise test is important in both statistical theories and applications, where the dimension of the time series can be comparable to or exceed the length of the time series. This paper proposes…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
The $k$ principal points of a random vector $\mathbf{X}$ are defined as a set of points which minimize the expected squared distance between $\mathbf{X}$ and the nearest point in the set. They are thoroughly studied in Flury (1990, 1993),…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…