Related papers: Asymptotics of Distances Between Sample Covariance…
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…
This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…
In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…
The asymptotic efficiency of the spatial sign covariance matrix (SSCM) relative to affine equivariant estimates of scatter is studied in detail. In particular, the SSCM is shown to be asymptoticaly inadmissible, i.e. the asymptotic…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…
Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Distributed compressive sensing is a framework considering jointly sparsity within signal ensembles along with multiple measurement vectors (MMVs). The current theoretical bound of performance for MMVs, however, is derived to be the same…
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states…
We consider the asymptotic joint distributions among several families of well-known metrics on $S_n$, the symmetric group. These include the bi-invariant metrics such as the Cayley and Hamming distance, and the left-invariant metrics such…
A natural (yet unconventional) test for goodness-of-fit measures the discrepancy between the model and empirical distributions via their Euclidean distance (or, equivalently, via its square). The present paper characterizes the statistical…