A0806
Title: Pseudo sufficient dimension reduction with ill-conditioned sample covariance matrix
Authors: Wenbo Wu - University of Texas at San Antonio (United States) [presenting]
Abstract: 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 an $n << p$ 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 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.