Abstract
This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples n and their 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 x1, . . ., xn are identically and independently generated from the Gaussian distribution N(0,I), the operator norm of the difference between a properly scaled Tyler's M-estimator and ∑i=1nxixi⊤/n tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges weakly to the Marčenko-Pastur distribution.
Original language | English (US) |
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Pages (from-to) | 114-123 |
Number of pages | 10 |
Journal | Journal of Multivariate Analysis |
Volume | 149 |
DOIs | |
State | Published - Jul 1 2016 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty
Keywords
- Covariance estimation
- Random matrix theory
- Robust statistics