Semiparametric Efficient Dimension Reduction in multivariate regression with an Inner Envelope

TL;DR

This paper introduces a semiparametric version of the inner envelope technique for multivariate regression, enhancing robustness and efficiency without relying on strict model assumptions.

Contribution

It develops a semiparametric inner envelope method that is both robust and efficient, extending the original technique beyond linear and normality assumptions.

Findings

The proposed method achieves global and local efficiency.

Simulation studies demonstrate robustness and improved performance.

Real data analysis confirms practical effectiveness.

Abstract

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However, their technique relied on a linear model with normally distributed error, which may be violated in practice. In this work, we propose a semiparametric variant of the inner envelope that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. Our simulations and real data analysis show that our method is both robust and efficient compared to existing dimension reduction methods in a diverse array of settings.