Skewing methods for variance-stabilizing local linear regression estimation

Abstract

It is known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct the problem, Nishida and Kanazawa proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of three SK estimators (the CC estimator) to eliminate bias terms. In this study, we show the CC estimator can also produce constant estimator variance by adjusting its weighting parameter and compare the performances of the two VS methods by simulations.

Keywords:

• Bandwidth selection
• Local linear regression estimator
• Local variable bandwidth
• Variance-stabilization
• Skewing methods

Acknowledgments

This study is financially supported by Japan Society for the Promotion of Science under a Grant-in-Aid for Young Scientists (B) JP16K17142 and a Grant-in-Aid for Scientific Research (C) 26520110, and by HUHS Grant-in-Aid for Scientific Research.