Kernel Estimators for Univariate Binary Regression

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Abstract
We present a rather thorough investigation of the use of kernel-based nonparametric estimators of the binary regression function in the case of a single covariate. We consider various versions of Nadaraya–Watson and local linear estimators, some involving a single bandwidth and others involving two bandwidths. The locally linear logistic estimator proves to be a good single-bandwidth estimator, although the basic Nadaraya–Watson estimator also fares quite well. Two-bandwidth methods show great potential when bandwidths are selected with knowledge of the target function, but much of their potential vanishes when data-based bandwidths are used. Likelihood cross-validation and plug-in approaches are the data-based bandwidth selection methods tested; both prove quite useful, with a preference for the latter. Adaptive two-bandwidth methods retain particularly good performance only in certain special situations (and separate estimation of the two bandwidths as for optimal density estimation is never recommended...

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