Wavelet-based estimation in a semiparametric regression model

Abstract

In this paper, we introduce a wavelet-based method for estimating the effective dimension reduction (EDR) space in the semiparametric regression model introduced by Li [Sliced inverse regression for dimension reduction, J. Amer. Statist. Assoc. 86 (1991) 316–327]. This method is obtained by using linear wavelet estimators of the density and regression functions that are involved in the covariance matrix of conditional expectation whose eigenvectors span the EDR space. Then, consistency of the proposed estimators is proved. A simulation study that allows one to evaluate the performance of the proposal with comparison to existing methods is presented.