Estimation Strategies for Censored Lifetimes with a Lexis-Diagram Type Model

Authors: BRUNEL, ELODIE¹; COMTE, FABIENNE²; GUILLOUX, AGATHE³

Source: Scandinavian Journal of Statistics, Volume 35, Number 3, September 2008 , pp. 557-576(20)

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Abstract:

When collecting right-censored lifetime data, a sampling bias occurs in many situations. The present authors offer a new sampling scheme description based on the Lexis diagram, which includes time-window and cohort studies. This implies a selection bias for the data collected. We also assume that censoring may occur. Hence, we provide a model selection strategy to estimate the hazard and density functions in this model. Adaptive projection estimators on trigonometric bases are developed by contrast penalization and optimal non-parametric rates of convergence are given. Both estimators are practically studied through simulation experiments as well as real data in the case of the time-window study.

Keywords: adaptive estimation; biased data; hazard rate; Lexis diagram; non-homogeneous Poisson process; non-parametric penalized contrast estimator; right censoring

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2007.00590.x

Affiliations: 1: 13M, Montpellier 2 University 2: MAP5, Paris Descartes University 3: LSTA, Paris 6 University

Publication date: 2008-09-01