ISIR: Independent Sliced Inverse Regression

Abstract

In this paper we consider a semiparametric regression model involving a p-dimensional explanatory variable x and including a dimension reduction of x via an index B′x. In this model, the main goal is to estimate B and to predict the real response variable Y conditionally to x. A standard approach is based on sliced inverse regression (SIR). We propose a new version of this method: the independent sliced inverse regression. The purpose of the regression of a univariate response y on a p-dimensional predictor vector x is to make inference on the conditional distribution of y|x. Following [17], x can be replaced by its standardized version z = [Σx](x− μx) , (1) where μx and Σx denote the mean and covariance matrix of x respectively assuming non-singularity of Σx. The goal of dimension reduction in regression is to find out a p × d matrix B such that

Cite this paper

@inproceedings{Li2013ISIRIS, title={ISIR: Independent Sliced Inverse Regression}, author={Kevin B. Li}, year={2013} }