Strong uniform consistency of the conditional hazard function with functional explanatory variable in single functional index model under randomly truncated data

The aim of this paper is to estimate non-parametrically the conditional hazard function of a scalar response variable taking values in separable Hilbert space. The response variable is assumed to be left truncated data. We introduce kernel-type estimators for the conditional distribution function and conditional density. Then, we establish the pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimators, based on the single index structure. Additionally, the asymptotic properties of the conditional hazard function are provided. Finally, a simulation study is carried to illustrate the performance of our estimator.