<div dir="ltr"><div><div><br></div>Hi Folks,<br></div><div>Hope everyone had a good spring break.<br><br></div><div>Randolf Altmeyer will present the next YPNG:<br>
<br>
Title: Estimating the spectrum of a covariance matrix using random matrix theory<br>
<br>
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.<br>
<br>
See you Friday in the Stat's classroom at 11am.<br>
<br>
Regards,<br>
sekhar<br><br><div class="gmail_quote"><div> </div></div></div></div>