Kernel regression for binary response data

This paper is based on the author's thesis, \Kernel Regression for Binary Response Data. We consider kernel-based estimators with additional weights of the regression functions in nonparametric binomial and binary regressions. Firstly, in the binomial regression with a single covariate and a xed covariate design, we introduce a weighted Nadaraya-Watson estimator and its bias adjusted estimator discussed in Okumura and Naito [13]. Secondly, in the binary regression with multiple covariates and a random covariate design, we propose weighted local linear estimators.