[YPNG] YPNG 9 Oct 2015

[sekhar]

Hi Folks,

This week Chao Gao will present in the YPNG seminar:

Title: Robust covariance matrix estimation

Abstract: I am going to give the motivation by discussing a simple location
estimation problem under Huber’s contamination model. I will argue that
Huber’s contamination model is a much better framework for robust 
statistics
than Hampel’s breakdown point. Under Huber’s framework, Tukey’s location
estimator is shown to be superior than the naive coordinate median. For the
robust covariance matrix estimation problem, I will introduce a new concept
called matrix depth, which is inspired by Tukey’s location depth. I will 
argue
that by maximizing the matrix depth function, we can obtain a good robust
covariance estimator that is minimax optimal under various high-dimensional
settings. Finally, I will give a general minimax theory for Huber’s 
contamination
model. The general minimax rate involves an interesting term that 
characterizes
the influence of the outliers. It coincides with modulus of continuity 
defined by
Donoho. Part of the talk is based on the paper: 
https://urldefense.proofpoint.com/v2/url?u=http-3A__arxiv.org_pdf_1506.00691.pdf&d=AwID-g&c=-dg2m7zWuuDZ0MUcV7Sdqw&r=V5RFj177zl_uvedej4jPpETqRnYdqAikrafH3LeyUoc&m=hWRiwereaKq5E9QLWijuued05IFwedsHqycl1YXK51s&s=xE5J7HWIoWAhQc4W7JertfGtalU_zlW3PSU4oDEo48Y&e= 

See you Friday in the Stat's classroom at 11am.

Regards,
sekhar