Skewing Methods for Variance-Stabilizing Local Linear Regression Estimation

Kiheiji Nishida

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arXiv · 1704.04356

Skewing Methods for Variance-Stabilizing Local Linear Regression Estimation

Kiheiji Nishida

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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.

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Kiheiji Nishida. 2017-04-14. Skewing Methods for Variance-Stabilizing Local Linear Regression Estimation. https://arxiv.org/abs/1704.04356

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