[YPNG] YPNG 1 April 2016

Sekhar Tatikonda sekhar.tatikonda at yale.edu
Mon Mar 28 12:44:29 EDT 2016

Hi Folks,
Hope everyone had a good spring break.

Randolf Altmeyer will present the next YPNG:

Title: Estimating the spectrum of a covariance matrix using random matrix

Abstract: Assume that we are given n iid observations of a p-dimensional
vector. Our goal is to do inference on the covariance matrix. In many
applications the sample size is of the same order as the dimension of the
observations. In this case the sample covariance matrix performs poorly and
it is necessary to find different assumptions for useful inference. For
instance, in the past under sparsity assumptions on the covariance matrix
minimax rates have been established. In this talk I will focus on a quite
different setting. Instead of sparsity, I assume that the empirical
distribution of the eigenvalues of the covariance matrix converges weakly
to some measure. The goal is then to do inference on the distribution of
the spectrum, rather than inference on single eigenvalues. This is the
setting of the classical Theorem of Marchenko-Pastur which is a key result
from random matrix theory. In my talk I will review this theorem and some
necessary tools, e.g. the Stieltjes transform. In the end, I will present
first steps towards establishing minimax rates for inference on the
spectral distribution.

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

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