On the Nonparametric Estimation of the Functional ψ-Regression for a Random Left-Truncation Model

Abstract

In this article we study a family of nonparametric estimators for the ψ-regression model when the response variable is subject to left-truncation by another random variable. Under standard assumptions, we get the almost complete convergence rate as well as asymptotic normality of the construct estimators. The obtained asymptotic normality permits getting a confidence interval usable in practice. Some simulations are drawn to illustrate the main results.

AMS Subject Classification:

• 60G42
• 62F12
• 62G20
• 62G05

Keywords:

• Asymptotic normality
• Functional data
• Kernel estimator
• Lynden–Bell estimator
• Robust estimation
• Small balls probabilities
• Strong consistency
• Truncated data

Acknowledgments

The authors are grateful to the two anonymous reviewers for their particularly careful reading, relevant remarks, and constructive comments, which helped the authors to improve the quality, adding the simulations part and the presentation of an earlier version of this article.