Title: Skewing Methods for Variance-Stabilizing Local Linear Regression Estimation,
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.