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