Asymptotic normality of a conditional hazard function estimate in the single index for quasi-associated data

Abstract

The main goal of this paper is to study the estimation of the conditional hazard function of a scalar response variable Y given a hilbertian random variable X in functional single-index model. We construct an estimator of this nonparametric function and we study its asymptotic properties, under quasi-associated structure. Precisely, we establish the asymptotic normality of the constructed estimator. We carried out simulation experiments to examine the behavior of this asymptotic property over finite sample data.

Keywords:

• Asymptotic normality
• conditional hazard function
• nonparametric kernel estimation
• quasi-association
• single-functional index model

Mathematics Subject Classification:

• 60G25
• 62G05
• 62G08
• 62G20
• 62N02

Acknowledgements

The authors would like to thank the Associate-Editor and thee anonymous reviewers for their valuable comments and suggestions which improved substantially the quality of this paper.