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.

KEYWORDS:

• Bandwidth selection
• Kolmogorov-Smirnov test
• least square cross-validation
• mixed-data

JEL CLASSIFICATION:

• C01
• C13
• C14

Acknowledgments

Racine would like to thank the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) for their ongoing support and to gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC:www.nserc.ca) and from the Social Sciences and Humanities Research Council of Canada (SSHRC:www.sshrc.ca). Hongjun Li’s research is partially supported by China National Science Foundation, project # 71601130.