Nonparametric conditional survival function estimation and plug-in bandwidth selection with multiple covariates

Abstract

The present research provides two methodological advances, simulation evidence and a real data analysis, all contributing to the area of local linear survival function estimation and bandwidth selection. The first contribution is the development of a double smoothed local linear survival function estimator which admits an arbitrary number of covariates and the analytic establishment of its asymptotic properties. The second contribution is the efficient implementation of the estimator in practice. This is achieved by developing an automatic plug-in smoothing parameter selector which optimizes the estimator’s performance in all coordinate directions. The traditional problem of vectorization of higher-order derivatives which lead to increasingly intractable matrix algebraic expressions is addressed here by introducing an alternative vectorization that exploits the analytic relationships between the functionals involved. This yields simpler, tractable and efficient in terms of computing time expressions which greatly facilitate the implementation of the rule in practice. The analytic study of the rule’s rate of convergence shows that in contrast to the traditional cross validation approach, the proposed bandwidth selector is functional even for a large number of covariates. The benefits of all methodological advances are illustrated with the analysis of a motivating real-world dataset on credit risk.