Cross-validated mixed-datatype bandwidth selection for nonparametric cumulative distribution/survivor functions

ABSTRACT

We propose a computationally efficient data-driven least square cross-validation method to optimally select smoothing parameters for the nonparametric estimation of cumulative distribution/survivor functions. We allow for general multivariate covariates that can be continuous, discrete/ordered categorical or a mix of either. We provide asymptotic analysis, examine finite-sample properties through Monte Carlo simulation, and consider an illustration involving nonparametric copula modeling. We also demonstrate how the approach can also be used to construct a smooth Kolmogorov–Smirnov test that has a slightly better power profile than its nonsmooth counterpart.