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Comparing Censoring and Random Truncation via Nonparametric Estimation of a Distribution Function

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Statistical Challenges in Modern Astronomy II

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Abstract

The Kaplan-Meier estimator and the Lynden-Bell estimator of a distribution function play pivotal roles in the nonparametric analysis of incomplete data. The former is constructed with a right-censored sample of lifetimes and the latter with a randomly truncated sample. Although both estimators look similar in their product-limit forms, they are quite different in distributional properties, especially the variances.

We use these two estimators to compare censoring and truncation. We first consider four models for incomplete data: the right-censoring model, the random truncation model, and two of their generalizations, the censoring-truncation model and the double censoring model. The generalizations are introduced to contrast the first two which are our focus. By way of comparison, we discuss model identifiability, hazard functions, a unified way of constructing nonparametric estimator of the distribution function by using an inversion formula, some of the difficulties in the application of the method, and some recent results particularly on random truncation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Grace L. Yang

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  1. Grace L. Yang
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Editors and Affiliations

  1. Department of Statistics, Pennsylvania State University, University Park, PA, 16802, USA

    G. Jogesh Babu

  2. Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA, 16802, USA

    Eric D. Feigelson

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© 1997 Springer Science+Business Media New York

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Yang, G.L. (1997). Comparing Censoring and Random Truncation via Nonparametric Estimation of a Distribution Function. In: Babu, G.J., Feigelson, E.D. (eds) Statistical Challenges in Modern Astronomy II. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1968-2_5

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  • DOI: https://doi.org/10.1007/978-1-4612-1968-2_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7360-8

  • Online ISBN: 978-1-4612-1968-2

  • eBook Packages: Springer Book Archive

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