Wednesday, August 22, 2018 - 13:00 in ZiF
Random matrices and high-dimensional inference
A talk in the Keine Reihe series by
Alexey Naumov from Moscow State University
| Abstract: |
Let $X_1,...,X_n$ be an independent identically distributed sample
in $\mathbb{R}^p$ with zero mean and unknown covariance matrix $\Sigma$. The problem
of recovering $\Sigma$ and its spectral projectors from these observations
naturally arises in many applications. In the first part of the talk, I
will give an overview of the recent results and techniques on covariance
matrix estimation based on the matrix Bernstein inequality,
Sudakov-Fernique’s inequality, Stein’s lemma etc. In the second part
of the talk, we will discuss estimation of the spectral projectors and
data-driven procedures for building sharp confidence sets. The talk will
be partially based on the joint results with F. Goetze, V. Spokoiny and
V. Ulyanov.
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