Scholarly Colloquia and Events

  • 10/27 Statistics Colloquium, Prof. Alex Shkolnik

    STATISTICS COLLOQUIUM

     

    Alex Shkolnik

    Assistant Professor

    Department of Statistics and Applied Probability

    University of California, Santa Barbara

     

     James Stein estimation for Principle Component Analysis

     

    Abstract

     

    The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the "usual estimator", may be suboptimal in high dimensions. The development of the James-Stein estimator, that addresses this paradox, has by now inspired a large literature on the theme of "shrinkage" in statistics. In this direction, we develop a James-Stein type estimator for the first principal component of a high dimension and low sample size data set. This estimator shrinks the usual estimator, an eigenvector of a sample covariance matrix under a spiked covariance model, and yields superior asymptotic guarantees. Our derivation draws a close connection to the original James-Stein formula so that the motivation and recipe for shrinkage is intuited in a natural way. Time permitting, we will explore the performance of the estimator on numerical examples and discuss several extensions including arbitrary shrinkage targets, weighted procedures and connections to quadratic programming.

     

    Bio: Dr. Alex Shkolnik is an assistant professor in the Department of Statistics and Applied Probability at UC Santa Barbara. He obtained his Ph.D. in Computational Mathematics & Engineering from Stanford University in 2015. His thesis work centered on computational methods for models used in the quantification and management of credit risk. Dr. Shkolnik's expertise lies in transform and Monte Carlo methods for the estimation and prediction of these risks. In particular, his ongoing focus is on the development of importance sampling techniques for complex systems encountered in finance and other research areas.

     

    Wednesday, October 27, 2021

    4:00 p.m. EDT, 1-hour duration

     

     

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    For more information, contact: Tracy Burke at tracy.burke@uconn.edu