Date: 2016-11-11

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Given a data set, Tyler’s M-estimator is a widely used covariance matrix estimator with robustness to outliers or heavy-tailed distribution. We will discuss two recent results of this estimator. First, we show that when a certain percentage of the data points are sampled from a low-dimensional subspace, Tyler’s M-estimator can be used to recover the subspace exactly. Second, in the high-dimensional regime that the number of samples n and the dimension p both go to infinity, p/n converges to a constant y between 0 and 1, and when the data samples are identically and independently generated from the Gaussian distribution N(0,I), we showed that the difference between the sample covariance matrix and a scaled version of Tyler’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. The second part is joint work with Xiuyuan Cheng and Amit Singer.

Speaker

Teng Zhang is an Assistant Professor in the Department of Mathematics at the University of Central Florida.