A Wavelet Estimator of the Intensity Function with Censored Data

Abstract

In reliability life-testing experiments and in medical studies, the interest often focuses on estimating the intensity function of the time to occurrence of some event of interest (such as engine failure, heart attack). Numerous methods have been developed for that purpose. Wavelets have recently become a widely used tool for nonparametric curve estimation. Their use for estimating intensity functions in the industrial and medical settings is however still limited. In this paper, we attempt to open the wavelet techniques to a broader audience, by providing a short introduction to the basic foundations of wavelets, and by describing a simple wavelet estimator for the intensity function of a random failure time. We consider the case where the random time is subject to right-censoring, as is usual in industrial life-testing and medical follow up. Asymptotic properties of this estimator are discussed using new arguments.

Key Words:

• Censored data
• consistency
• failure time data
• intensity function
• mean integrated square error
• wavelet estimation

Additional information

Notes on contributors

Jean-Francois Dupuy

Jean-Francois Dupuy is a Professor of Statistics at the Laboratory of Applied Mathematics of La Rochelle University (France). His research interests include semi-parametric inference, regression analysis, and failure time data analysis.

Kossi Essona Gneyou

Kossi Essona Gneyou is an Associate Professor at the Department of Mathematics of Lome University (Togo). His research interests include empirical processes, non-parametric statistic, and failure time data analysis.