[Ml-stat-talks] ORFE Colloquium: Tony Cai (UPenn)
rigollet at Princeton.EDU
Tue Nov 22 09:50:16 EST 2011
Tony Cai will be speaking today at the ORFE Colloquium. Tony is the current editor in chief of the Annals of Statistics. He has made significant contributions to the theory of nonparametric estimation and more recently high-dimensional statistics.
Details of his talk are given below.
=== ORFE Colloquium Announcement ===
DATE: Today, November 22, 2011
LOCATION: Room 101, Sherrerd Hall
SPEAKER: T. Tony Cai, The Wharton School, University of Pennsylvania
TITLE: Adaptive Estimation of Large Covariance Matrices
ABSTRACT: Covariance structure is of fundamental importance in many areas of statistical
inference and a wide range of applications, including genomics, fMRI analysis, risk management,
and web search problems. Estimation of large covariance matrices has drawn considerable
recent attention and the theoretical focus so far is mainly on developing a minimax theory over
a fixed parameter space. In this talk, I will discuss some recent results on adaptive estimation of
covariance matrices in the highdimensional setting. The goal is to construct a single procedure
which is minimax rate optimal simultaneously over each parameter space in a large collection. We
shall begin with adaptive estimation of bandable covariance matrices. A fully data driven block
thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample
covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding.
The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices.
In addition, adaptive estimation of sparse covariance matrices will also be discussed.
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