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Activity Number: 331
Type: Invited
Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #314644 View Presentation
Title: Uniform Post Selection Inference for Median Regression and Other Z-Estimation Problems
Author(s): Victor Chernozhukov* and Alexandre Belloni and Kengo Kato
Companies: MIT and Duke University and The University of Tokyo
Keywords: post-selection ; inference ; honest ; uniform validity ; z-estimation ; high dimensions
Abstract:

We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse least absolute deviation/median regression model. Our new methods are based on optimal estimating equations immunized against non-regular estimation of the nuisance parameters in the sense of Neyman. We establish that the estimator of a single regression coefficient is asymptotically root-n consistent and normal uniformly with respect to the underlying sparse model. The resulting confidence regions are valid uniformly with respect to the underlying model. We then generalize our method to the case where many (d > n) regression coefficients are of interest in a non-smooth Z-estimation framework with approximately sparse nuisance functions, containing median regression with a single target regression coefficient as a very special case. We construct simultaneous confidence bands on all d> n coefficients, and establish their uniform validity over the underlying approximately sparse model. Joint work with Kengo Kato and Alexandre Belloni. arXiv:1304.0282


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