Slice Weighted Average Regression

TL;DR

This paper introduces a sliced weighted average regression method that enhances robustness and flexibility in estimating single-index models, outperforming traditional least squares in various scenarios.

Contribution

It proposes a novel sliced least-squares estimator that improves robustness and allows for multiple directions, extending the applicability of single-index models.

Findings

The new estimator is simple to implement and more robust than ordinary least squares.

Simulation studies show significant improvements in estimation accuracy.

Real data examples demonstrate practical advantages over existing methods.

Abstract

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this paper we propose a new sliced least-squares estimator that utilizes ideas from Sliced Inverse Regression. Slices with problematic observations that contribute to high variability in the estimator can easily be down-weighted to robustify the procedure. The estimator is simple to implement and can result in vast improvements for some models when compared to the usual least-squares approach. While the estimator was initially conceived with the single-index model in mind, we also show that multiple directions can be obtained, therefore providing another notable advantage of using slicing with least squares. Several simulation studies and a real data example are included, as well as some comparisons with some other recent methods.