This paper is concerned with nonparametric binomial regression. A kernel-based binomial regression estimator and its bias-adjusted version are proposed, of which kernel is weighted by the inverse of a variance estimator of the observed proportion at each covariate. It is shown that the asymptotic normality of the bias-adjusted estimator holds under some regularity conditions. The proposed estimators and other estimators discussed by several authors are compared through their asymptotic MSEs. From these considerations, together with the simulation results, advantages of our weighting scheme are reported.
