Rate of convergence in probability to the Marchenko-Pastur law

On the Rate of Convergence to the Marchenko–Pastur Distribution

LetX = (Xjk) denote n×p random matrix with entriesXjk, which are independent for 1 ≤ j ≤ n, 1 ≤ k ≤ p. We consider the rate of convergence of empirical spectral distribution function of matrix W = 1 p XX ∗ to the Marchenko–Pastur law. We assume that EXjk = 0, EX 2 jk = 1 and that the distributions of the matrix elements Xjk have a uniformly sub exponential decay in the sense that there exists a...

A total positivity property of the Marchenko-Pastur Law

Marchenko-Pastur Law for Tyler’s and Maronna’s M-estimators

This paper studies the limiting behavior of Tyler’s and Maronna’s Mestimators, in the regime that the number of samples n and the dimension p both go to infinity, and p/n converges to a constant y with 0 < y < 1. We prove that when the data samples are identically and independently generated from the Gaussian distribution N(0, I), the difference between the sample covariance matrix and a scaled...

On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions

In this paper, we prove a result linking the square and the rectangular R-transforms, which consequence is a surprising relation between the square and rectangular free convolutions, involving the Marchenko-Pastur law. Consequences on infinite divisibility and on the arithmetics of Voiculescu’s free additive and multiplicative convolutions are given.

the investigation of research articles in applied linguistics: convergence and divergence in iranian elt context

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