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.