Weighted Kernel Estimators in Nonparametric Binomial Regression

This paper is concerned with nonparametric binomial regression. Two kernel-based binomial regression estimators and their bias-adjusted versions are proposed, whose kernels are weighted by the inverses of variance estimators of the observed proportion at each covariate. Asymptotic theories for deriving asymptotic mean squared errors (AMSEs) of proposed estimators are developed. Comparisons with other estimators discussed by several authors are implemented through the AMSEs. From these considerations, together with the simulation results, the advantages of our weighting scheme are reported.