Skewing Methods for Variance-Stabilizing Local Linear Regression Estimation

TL;DR

This paper compares variance-stabilizing and skewing methods for local linear regression, showing that skewing can sometimes outperform variance stabilization in achieving constant estimator variance.

Contribution

It introduces a comparison between two variance stabilization techniques for convex combination estimators in local linear regression.

Findings

Skewing methods can outperform variance-stabilizing bandwidths in certain cases.

The weighting approach can achieve better variance stabilization without local bandwidth adjustment.

Performance depends on specific data and estimator configurations.

Abstract

It is well-known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall (1998) proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of one LL estimator and two SK estimators that are symmetrically placed on both sides of the LL estimator (the convex combination (CC) estimator) to eliminate higher-order terms in its asymptotic bias. To obtain a CC estimator with a constant estimator variance without employing the VS local variable bandwidth, the weight in the convex combination must be determined locally to produce a constant estimator variance. In this study, we compare the performances of two VS methods for a CC estimator and find cases in which the weighting method can superior to the VS bandwidth method in terms of the degree of variance stabilization.