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Home | Seminars and Symposia | Past seminars/symposia: Thursday, October 23, 2014

DTC Seminar Series

Marcenko-Pastur Law for Tyler's and Maronna's M-estimators

by

Teng Zhang
The Program in Applied & Computational Mathematics
Princeton University

Thursday, October 23, 2014
9:40 a.m. reception
10:10 a.m. seminar

401/402 Walter Library

In this talk we consider the limiting behavior of Tyler's and Maronna's M-estimators, 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 less than y less than 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 version of Tyler's M-estimator or Maronna's M-estimator tends to zero in spectral norm, and the empirical spectral densities of both estimators converge to the Marcenko-Pastur distribution. We also prove that when the data samples are generated from an elliptical distribution, the limiting distribution of Tyler's M-estimator converges to a Marcenko-Pastur-Type distribution. This is joint work with Xiuyuan Cheng and Amit Singer.

 

Teng Zhang received his B.S. degree in Mathematics from Fudan University, China, in 2006, and the Ph.D. degree in Mathematics from University of Minnesota, Minneapolis, MN, USA, in 2011. From September 2011 to January 2012, he was a Postdoctoral Fellow at Institute for Mathematics and its Applications (IMA), Minneapolis, MN. He is currently a postdoctoral researcher affiliated with the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.