Nonparametric estimation of a regression function from backward recurrence times in a cross-sectional sampling

This study considers the nonparametric estimation of a regression function when the response variable is the waiting time between two consecutive events of a stationary renewal process, and where this variable is not completely observed. In these circumstances, our data are the recurrence times from the occurrence of the last event up to a pre-established time, along with the corresponding values of a certain set of covariates. Estimation of the error density function and some of its characteristics are also considered. For the proposed estimators, we first analyze their asymptotic behavior and, thereafter, carry out a simulation study to highlight their behavior in finite samples. Finally, we apply this methodology to an illustrative example with biomedical data.