The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations

Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of different order. We derive a similar estimator in the context of local (multivariate) estimation based on estimating functions. As expected, this lower order bias is bought at a cost of increased variance. Surprisingly, when compared to ordinary kernel and local linear kernel estimators, the bias-corrected estimators increase variance by a factor independent of the problem, depending only on the kernel used. The variance increase is approximately 40% and more for kernels in standard use. However, the variance increase is still less than that incurred when undersmoothing a local quadratic regression estimator. -- Bootstrap ; Nonparametric Regression ; Estimating Equations ; Generalized Linear Models ; Local Linear Regression ; Bias Reduction