题 目：On Distribution Weighted Partial Least Squares with Diverging Number of Highly Correlated

Predictors

报告人：Prof.Li-Xing Zhu

Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

时 间：2008年6月3日（周二）上午10：00-11：00

地 点：伟易博202

Abstract

Because highly correlated data arise from many scientific fields, in this paper we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. To this end, we first develop a distribution weighted least squares estimator (DWLSE) that can recover directions in central subspace (CS), then use DWLSE as a seed vector and project it onto a Krylov space by partial least squares to avoid computing the inversion of the covariance of predictors. Thus, such a distribution weighted partial least squares (DWPLS) can handle the cases with high-dimensional and highly corrected predictors. Furthermore, we also suggest an iterative algorithm for obtaining a better initial value before implementing PLS. Strong consistency and asymptotic normality of the estimates are also achieved when the dimensionpof predictors is of convergence rateO(n1=2=logn) andO(n1=3) respectively wherenis the sample size. When there are no other constraints on the covariance of predictors, the ratesn1=2 andn1=3 are optimal. We also propose a BIC type criterion to estimate the dimension of the Krylov space in the PLS procedure. Illustrative examples by a real data set and comprehensive simulations demonstrate that the method is robust to non-ellipticity, and works well even in \smalln, largep" problems.