Estimation on inverse regression using principal components of covariance matrix of sliced data

Abstract

Li (1991) introduced the so called sliced inverse regression (SIR) which reduces the dimension of the input variable in regression analysis, without any modelfitting process. Akita et al. (2009) proposed an improvement of SIR, called SIR, which uses conditional covariate matrices. In this paper, developing the approach of PCASIR, we propose yet another improvement of SIR, which we call PCA-SIR2. Simulation results produced by SIR, PCA-SIR and PCA-SIR2 are compared.