A Principal Square Response Forward Regression Method for Dimension Reduction

TL;DR

This paper proposes a new dimension reduction method called PSRFR for high-dimensional data, demonstrating its theoretical properties, robustness, and effectiveness through simulations and real-world data analysis.

Contribution

The paper introduces PSRFR, a novel SDR method with proven consistency, asymptotic properties, and improved performance in complex high-dimensional scenarios.

Findings

PSRFR outperforms existing methods in simulations.

It is robust to heteroscedasticity and elliptical distributions.

Effective in real-world wine quality dataset analysis.

Abstract

Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for estimating the central subspace of the response variable Y, given the vector of predictor variables $\bm{X}$. We provide a computational algorithm for implementing PSRFR and establish its consistency and asymptotic properties. Monte Carlo simulations are conducted to assess the performance, efficiency, and robustness of the proposed method. Notably, PSRFR exhibits commendable performance in scenarios where the variance of each component becomes increasingly dissimilar, particularly when the predictor variables follow an elliptical distribution. Furthermore, we illustrate and validate the effectiveness of PSRFR using a real-world dataset concerning wine quality. Our findings underscore the utility and reliability of the PSRFR method in practical applications of dimension reduction for high-dimensional data analysis.