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Activity Number: 288 - New Insights from Classical Wisdom—honoring Lawrence D. Brown’s Contributions to Graduate Student Education
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #302901 Presentation
Title: Randomness-Free Study of Smooth M-Estimators
Author(s): Arun Kuchibhotla*
Companies: University of Pennsylvania
Keywords: M-estimators; Taylor Series; Newton-Kantorovich; post-selection inference

Almost all of large sample theory in statistics/econometrics/machine learning begin with a specific randomness structure on the data like iid or uniform mixing observations and so on. The basic tool for asymptotics normality however is the Taylor series expansion which is deterministic in nature. Following this line of thought we provide bounds on estimation error and linear (Bahadur) representation error for M-estimators that are deterministic. These results are finite sample (non-asymptotic) and applies to any realization of data without any assumption on independence and dependence. Newton-Kantorovich theorem plays a pivotal role in this. After a discussion of these results in the talk, we provide applications to cross-validation, sub-sampling and post-selection inference. This talk is based on

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

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