A Wavelet Estimator of the Intensity Function with Censored Data

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 be...

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Bibliographic Details
Published in:Quality technology & quantitative management 2011, Vol.8 (4), p.401-410
Main Authors: Dupuy, Jean-Francois, Gneyou, Kossi Essona
Format: Article
Language:English
Subjects:
Censored data
consistency
failure time data
intensity function
mean integrated square error
wavelet estimation
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Summary: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.
ISSN:1684-3703
1684-3703
DOI:10.1080/16843703.2011.11673266