Product limit estimates: A generalized maximum likelihood study

Mei Cheng Wang

doi:10.1080/03610928708829561

Product limit estimates: A generalized maximum likelihood study

Mei Cheng Wang

Bloomberg School of Public Health

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

The generalized maximum likelihood estimate (GMLE) assumptions are studied for four product-limit estimates (PLE): Censoring PLE (Kaplan-Meier estimate), truncation PLE, censoring-truncation PLE, and the degenerated PLE - the empirical distribution function. This paper shows that all the PLE's are also the GMLE's even if they are derived from partial likelihoods by natural parameterization techniques. However, a counter example is given to show that Kiefer Wolfowitz's assumption (1956) for consistency of GMLE can hardly be satisfied for undominated case.

Original language	English (US)
Pages (from-to)	3117-3132
Number of pages	16
Journal	Communications in Statistics - Theory and Methods
Volume	16
Issue number	11
DOIs	https://doi.org/10.1080/03610928708829561
State	Published - Jan 1 1987

Keywords

censoring
generalized maximum likelihood estimate
product-limit estimate
truncation

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610928708829561

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abstract = "The generalized maximum likelihood estimate (GMLE) assumptions are studied for four product-limit estimates (PLE): Censoring PLE (Kaplan-Meier estimate), truncation PLE, censoring-truncation PLE, and the degenerated PLE - the empirical distribution function. This paper shows that all the PLE's are also the GMLE's even if they are derived from partial likelihoods by natural parameterization techniques. However, a counter example is given to show that Kiefer Wolfowitz's assumption (1956) for consistency of GMLE can hardly be satisfied for undominated case.",

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AB - The generalized maximum likelihood estimate (GMLE) assumptions are studied for four product-limit estimates (PLE): Censoring PLE (Kaplan-Meier estimate), truncation PLE, censoring-truncation PLE, and the degenerated PLE - the empirical distribution function. This paper shows that all the PLE's are also the GMLE's even if they are derived from partial likelihoods by natural parameterization techniques. However, a counter example is given to show that Kiefer Wolfowitz's assumption (1956) for consistency of GMLE can hardly be satisfied for undominated case.

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KW - truncation

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Product limit estimates: A generalized maximum likelihood study

Abstract

Keywords

ASJC Scopus subject areas

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