Speaker: Kengo Kato, Cornell University
Title: "Berry-Esseen bounds for Chernoff-type non-standard asymptotics in isotonic regression"
Abstract: A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution appears as the distributional limit in many non-regular estimation problems, the accuracy of Chernoff-type approximations has been largely unknown. In this talk, I will discuss Berry-Esseen bounds for Chernoff-type limit distributions in the canonical non-regular statistical estimation problem of isotonic (or monotone) regression. The derived Berry-Esseen bounds match those of the oracle local average estimator with optimal bandwidth in each scenario of possibly different Chernoff-type asymptotics, up to multiplicative logarithmic factors. Our method of proof differs from standard techniques on Berry-Esseen bounds, and relies on new localization techniques in isotonic regression and an anti-concentration inequality for the supremum of a Brownian motion with a Lipschitz drift. This talk is based on the joint work with Qiyang Han.
Short bio: Kengo Kato is currently an associate professor in the Department of Statistics and Data Science at Cornell University. He obtained his Ph.D. at the University of Tokyo in 2009 and spent nine years as faculty in Japan before joining Cornell. He has been working on mathematical statistics and econometric, specifically quantile regression and distributional approximations in high dimensions. Faculty web page: https://stat.cornell.edu/people/faculty/kengo-kato
Seminar Date/Time: Thursday May 14th, 4:10pm
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