Bandwidth selection in marker dependent kernel hazard estimation

Practical estimation procedures for the local linear estimation of an unrestricted failure rate when more information is available than just time are developed. This extra information could be a covariate and this covariate could be a time series. Time dependent covariates are sometimes called markers, and failure rates are sometimes called hazards, intensities or mortalities. It is shown through simulations and a practical example that the fully local linear estimation procedure exhibits an excellent practical performance. Two different bandwidth selection procedures are developed. One is an adaptation of classical cross-validation, and the other one is indirect cross-validation. The simulation study concludes that classical cross-validation works well on continuous data while indirect cross-validation performs only marginally better. However, cross-validation breaks down in the practical data application to old-age mortality. Indirect cross-validation is thus shown to be superior when selecting a fully feasible estimation method for marker dependent hazard estimation.