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Activity Number: 471 - New Frontier in Developments of Complex-Structured High-Dimensional Data Analysis
Type: Topic Contributed
Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
Sponsor: International Chinese Statistical Association
Abstract #322663
Title: Pseudo Sufficient Dimension Reduction with Ill-Conditioned Sample Covariance Matrix
Author(s): Wenbo Wu*
Companies: The University of Texas at San Antonio
Keywords: dimension reduction; measurement errors

In high-dimensional data problems, the sample covariance matrix of the predictors is often singular either due to correlations among the predictors or due to a n < < p setting. Most sufficient dimension reduction methods rely on the inverse of the sample covariance as part of the estimation process. To conquer the challenge brought by the singular or near-singular sample covariance matrix, we propose a pseudo estimation approach by artificially adding random noises to the observed data. We show that with a careful control of the added noises, the resulting estimator based on the perturbed data can still be consistent. In addition, a new variable selection procedure is proposed based on the pseudo estimator. The advantages of the proposed method are demonstrated by both simulation studies and real data analyses.

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

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