seminars:datasci:191126
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revision | |||
| seminars:datasci:191126 [2019/10/31 18:44] – qyu | seminars:datasci:191126 [2019/10/31 18:45] (current) – qyu | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| + | <WRAP centeralign>## | ||
| + | |||
| + | * 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> | ||
| + | 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' | ||
| + | |||
| + | 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. | ||
| + | |||
| + | </ | ||