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

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  • ELODIE BRUNEL
  • FABIENNE COMTE
  • AGATHE GUILLOUX

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.

Suggested Citation

  • Elodie Brunel & Fabienne Comte & Agathe Guilloux, 2008. "Estimation Strategies for Censored Lifetimes with a Lexis‐Diagram Type Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 557-576, September.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:557-576
    DOI: 10.1111/j.1467-9469.2007.00590.x
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    References listed on IDEAS

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    1. Jens Lund, 2000. "Sampling Bias in Population Studies—How to Use the Lexis Diagram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 589-604, December.
    2. A. Antoniadis & G. Grégoire & G. Nason, 1999. "Density and hazard rate estimation for right‐censored data by using wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 63-84.
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