A Local Modal Outer-Product-Gradient Estimator for Dimension Reduction

TL;DR

This paper introduces a Local Modal Outer-Product-Gradient estimator for dimension reduction that effectively captures important data directions in the presence of skewed error distributions, improving robustness over traditional methods.

Contribution

It proposes a novel LMOPG method based on mode regression to better estimate the central subspace under skewed error distributions, with proven consistency and asymptotic normality.

Findings

Demonstrates the estimator's consistency and asymptotic normality.

Shows improved performance and robustness through Monte Carlo simulations.

Outperforms traditional OPG in skewed error scenarios.

Abstract

Sufficient dimension reduction (SDR) is a valuable approach for handling high-dimensional data. Outer Product Gradient (OPG) is an popular approach. However, because of focusing the mean regression function, OPG may ignore some directions of central subspace (CS) when the distribution of errors is symmetric about zero. The mode of a distribution can provide an important summary of data. A Local Modal OPG (LMOPG) and its algorithm through mode regression are proposed to estimate the basis of CS with skew errors distribution. The estimator shows the consistent and asymptotic normal distribution under some mild conditions. Monte Carlo simulation is used to evaluate the performance and demonstrate the efficiency and robustness of the proposed method.