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Activity Number: 5 - New Developments in Modern Statistical Theory
Type: Invited
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #300591
Title: On Least Squares Estimation under Heteroscedastic and Heavy-Tailed Errors
Author(s): Rohit Kumar Patra*
Companies: University of Florida

We consider least squares estimation in a general nonparametric regression model. We find upper bounds on the rates of convergence of the least squares estimator (LSE) of the unknown regression function when the errors have uniformly bounded conditional variance and have only finitely many (marginal) moments. We show that the interplay between the moment assumptions on the error, the metric entropy of the class of functions involved, and the ``smoothness'' of the function class around the truth drives the rate of convergence of the LSE. In all of this, we make no additional assumption on the dependence structure between the covariates and the unobserved errors. Our results are finite sample. This is joint work with Arun K. Kuchibhotla.

Authors who are presenting talks have a * after their name.

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