Online Program Home
My Program

Abstract Details

Activity Number: 247 - Sufficient Dimension Reduction and High-Dimensional Data
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #302884 Presentation
Title: Non Standard Asymptotics in High Dimension: Manski's Maximum Score Estimator Revisited
Author(s): Debarghya of Mukherjee* and Ya'acov Ritov and Moulinath of Banerjee
Companies: university of michigan and university of michigan and university of michigan
Keywords: Maximum Score Estimator; Censored linear model; High Dimension

Manski’s celebrated maximum score estimator for the censored response linear model has been the focus of much investigation in both the econometrics and statistics literature, but its behavior under growing dimension scenarios still largely remains unknown. This project seeks to address that gap. Two different cases are considered: p grows with n but at a slow rate (i.e. p/n goes to 0 ) and p >> n (fast growth). By relating Manski’s score estimation to empirical risk minimization in a classification problem, we studied its convergence properties under suitable margin condition. We have also established minimax bounds under both the regimes, which differ by a log factor. In slow growth regime, we have constructed an estimator which is minimax optimal. Finally we provide some computational recipes for the maximum score estimator in growing dimensions that shows promising result.

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

Back to the full JSM 2019 program