On the robust regression for a censored response data in the single functional index model

Abstract

Let ${(T_n)}_{n\ge 1}$ be an independent and identically distributed (iid) sequence of interest random variables (rv) distributed as T when the latter is subject to an independent censored rv C. In this work, we built and study a family of robust non parametric estimators for a regression function based on a kernel method. The covariates data are random functional type iid linked to single-index model. Under general conditions, we establish the pointwise almost sure convergence with rate an asymptotic normality of the estimator. The asymptotic standard deviation is explicitly given. By product, confidence bands are given and the special case is studied. Finally, simulations are drawn to illustrate both quality of fit and robustness.

Keywords:

• Asymptotic normality
• functional data
• functional Hilbert space
• Kaplan–Meier estimator
• Kernel estimate
• pointwise almost sure convergence
• robust regression
• single functional index model

AMS Subject Classification::

• 62G05
• 62G20

Acknowledgements

The authors are grateful to an anonymous referee whose careful reading gave them the opportunity to improve the quality of the paper.