The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data
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In this paper, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of a distribution function when the data are incomplete due to grouping, censoring and/or truncation.Abstract:
SUMMARY This paper is concerned with the non-parametric estimation of a distribution function F, when the data are incomplete due to grouping, censoring and/or truncation. Using the idea of self-consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. An application to hypothesis testing is indicated.read more
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References
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Nonparametric Estimation from Incomplete Observations
Edward L. Kaplan,Paul Meier +1 more
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Journal Article
Evaluation of survival data and two new rank order statistics arising in its consideration.
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Asymptotically Efficient Rank Invariant Test Procedures
Richard Peto,Julian Peto +1 more
Journal ArticleDOI
An empirical distribution function for sampling with incomplete information
TL;DR: In this article, it was shown that the consistency property of the maximum likelihood estimators depends on a grouping of observations which might very well appeal to an investigator on purely intuitive grounds.