Kernel Binary Regression with Multiple Covariates

Abstract

In this paper, we consider kernel-based estimators in the nonparametric binary regression problem with multidimensional covariates. We propose a local linear type estimator of the response probability function with kernel weighted at each observed covariate. In addition, we discuss the rule of thumb bandwidth selector and the plug-in bandwidth selector. The efficiency of the weighted local linear estimator is determined from results of asymptotic properties and our simulation study.

Pointwise comparison of two multivariate density functions

“…While our focus has been on comparison of densities, our results generalize. For example, our findings will apply to comparison of kernel binary regression estimators (e.g., Okumura, 2011; Signorini & Jones, 2004). This follows because the asymptotic rates for bias and variance of such estimators are inherited directly from the constituent kernel density estimators.…”