A new algorithm for estimating the effective dimension-reduction subspace

TL;DR

This paper introduces a new algorithm for estimating the effective dimension-reduction subspace in multi-index regression models, demonstrating its consistency and empirical performance.

Contribution

The paper proposes a novel procedure for recovering EDR subspace directions with proven $\

Findings

Algorithm achieves $\

Empirical results validate the method's effectiveness

Abstract

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is proposed. Under mild assumptions, $\sqrt n$-consistency of the proposed procedure is proved (up to a logarithmic factor) in the case when the structural dimension is not larger than 4. The empirical behavior of the algorithm is studied through numerical simulations.