Efficient estimation in sufficient dimension reduction

TL;DR

This paper introduces an efficient semiparametric estimation method for identifying the central subspace in sufficient dimension reduction, achieving optimal efficiency without distributional assumptions.

Contribution

It proposes a novel parameterization converting the problem into a finite-dimensional estimation, enabling an efficient estimator that reaches the semiparametric efficiency bound.

Findings

The estimator attains the optimal efficiency bound.

It performs well in simulations compared to existing methods.

The method is applicable to real data analysis.

Abstract

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions. Our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods.