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Bandwidth selection for kernel binomial regression

In nonparametric binomial regression, the weighted kernel estimator of the regression function and its efficient bias-adjusted version have been proposed by Okumura and Naito (2004) with consideration to differences of variances of observed response proportions at covariates. The aim of this article is to propose an effective data-based method for bandwidth selection of the bias-adjusted estimator. The proposed method is developed through three steps: the plug-in method by Ruppert et al. (1995), a scale adjustment suggested by Yang and Tschernig (1999), and an effective use of the approach discussed by Grizzel et al. (1969) for the rule-of-thumb part. Theoretical considerations on the asymptotic performance of the selected bandwidth are given under the situation where the numbers of covariates and responses observed at each covariate increase. (References: Okumura, H. and Naito, K., 2004, The weighted estimators in nonparametric binomial regression. Journal of Nonparametric Statistics, 16, 39–62; Ruppert, D., Sheather, S.J. and Wand, D.W., 1995, An effective band width selector for local least squares regression. Journal of the American Statistical Association, 90, 1257–1270; Yang, L. and Tschernig, R., 1999, Multivariate bandwidth selection for local linear regression. Journal of the Royal Statistical Society, 61, 793–815; Grizzel, J.E., Starmer, C.F. and Koch, G.G., 1969, Analysis of growth and dose-response curves. Biometrics, 25, 489–504.)