Optimal quantization applied to Sliced Inverse Regression

TL;DR

This paper introduces a novel approach combining sliced inverse regression with optimal quantization to improve estimation and prediction in semiparametric regression models involving dimension reduction.

Contribution

The paper proposes a new method integrating optimal quantization with SIR for better estimation of parameters and conditional distributions in semiparametric models.

Findings

Estimators converge reliably in simulations.

Method performs well with finite samples.

Improves dimension reduction accuracy.

Abstract

In this paper we consider a semiparametric regression model involving a $d$-dimensional quantitative explanatory variable $X$ and including a dimension reduction of $X$ via an index $\beta'X$. In this model, the main goal is to estimate the euclidean parameter $\beta$ and to predict the real response variable $Y$ conditionally to $X$. Our approach is based on sliced inverse regression (SIR) method and optimal quantization in $\mathbf{L}^p$-norm. We obtain the convergence of the proposed estimators of $\beta$ and of the conditional distribution. Simulation studies show the good numerical behavior of the proposed estimators for finite sample size.