seminars:datasci:191126 [Department of Mathematics and Statistics, Binghamton University]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.

<WRAP centeralign>##Data Science Seminar##\\ Hosted by Department of Mathematical Sciences</WRAP>

  * Date: Tuesday, November 26, 2017
  * Time: 12:00pm -- 1:00pm
  * Room: WH-100E
  * Speaker: Wei Yang (Binghamton University)
  * Title: Random Covariance Matrix and the Marchenko-Pastur law

<WRAP center box 80%>
<WRAP centeralign>**//Abstract//**</WRAP>
Let x be a p-dimensional centered random vector, with some un-
known covariance matrix Σ. Let x1 , · · · , xn be n i.i.d copies of x, we can form

S =sample mean of xi*xi's

Which is an example of a p×p random matrix. When {xi }_{i∈{n}} are realized, S is
just a sample covariance matrix. If n is large, S by the Law of Large number is
a good estimator for Σ. When the size n is limited, but n, p are comparable, the
classical Marchenko-Pastur (MP) Law says that , the eigenvalues of S follows
roughly the MP distribution.
In this talk, we are going to use the Stieltjes Transformation (Resolvent) method
to prove a version of the MP Law. The focus will be on the method of proof, a
common technique in the theory of Random Matrices.

</WRAP>