Comparing Nonparametric Estimators for Length-Biased Data

Abstract

Length-biased data appear when sampling lifetimes by cross-section. Right-censoring may affect the sampled information due to time limitation in following-up, lost to follow-up cases, etc. In this article, we compare by simulations two alternative nonparametric estimators of the lifetime distribution function when the data are length-biased and right-censored. These estimates, recently introduced in the literature, are based on nonparametric maximum-likelihood and moment-based principles. It is shown that the relative benefits associated to each estimator depend on several factors, such as the shape of the underlying distribution, sample size, or censoring level.

Keywords:

• Censoring
• Length-bias
• Moment-based estimator
• Nonparametric maximum likelihood

Mathematics Subject Classification:

• 62G05
• 62N01

Acknowledgments

J. de Uña-Álvarez was supported by the Grant MTM2005-01274 (FEDER funding included) of the Spanish Ministerio de Educación y Ciencia.