Online Program Home
  My Program

Abstract Details

Activity Number: 73 - Nonparametric Statistics in High-Dimensional Settings
Type: Contributed
Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #324698 View Presentation
Title: Finite Sample Breakdown Point for Sliced Inverse Regression
Author(s): Ulrike Genschel*
Companies: Iowa State University
Keywords: dimension reduction ; SIR ; subspaces ; robustness ; breakdown point

For dimension reduction procedures such as Sliced Inverse Regression (SIR) a worst possible case of data contamination can be defined as producing an estimated subspace that is maximally distant from the true dimension reduction subspace. That is, the estimated subspace is as orthogonal as possible to the true subspace. To formalize the concept of maximal distances between subspaces, we introduce a metric on subspaces. By metricizing distances between dimension reduction subspaces, worst case results for data contamination can be formulated to define a finite sample breakdown point as a measure of global robustness. We present the finite sample breakdown point for SIR and illustrate that the result depends intricately on a combination of factors, such as the dimension of the regressor space, the dimension of the true e.d.r. subspace, and whether the dimension is known or requires estimation. This study is further complicated by the issue that the most disruptive directions of contamination change between cases when the regressor covariance structure is known or unknown. Our theoretical findings are illustrated through simulation.

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

Back to the full JSM 2017 program

Copyright © American Statistical Association