Nonparametric Estimation from Incomplete Observations

@article{Kaplan1958NonparametricEF,
  title={Nonparametric Estimation from Incomplete Observations},
  author={Edward L. Kaplan and Paul Meier},
  journal={Journal of the American Statistical Association},
  year={1958},
  volume={53},
  pages={457-481}
}
  • E. Kaplan, P. Meier
  • Published 1 June 1958
  • Mathematics
  • Journal of the American Statistical Association
Abstract In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential… 

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References

SHOWING 1-10 OF 43 REFERENCES
Maximum Likelihood Estimation of the Parameters of a Normal Distribution which is Truncated at a Known Point
1. Introduction. The two cases where a normal distribution is “truncated” at a known point have been treated by R. A. Fisher (1) and W. L. Stevens (2), respectively. Fisher treated the case in which
The estimation of mortality and other decremental probabilities
Abstract The standard actuarial methods of estimating the age-specific one-year probabilities of death in a given community were developed—for the most part, many years ago-with large bodies of
Time-specific life table contrasted with observed survivorship.
In obtaining life tables for any group of individuals, biological or physical, there are two basically different types of observation which are commonly used. One of these consists in the
A synthesis of methods of deriving measures of decrement from observed data
OF THE DISCUSSION Mr W. G. Bailey, in introducing the paper, said it was with some trepidation that the authors presented a paper on such a subject. They had been investigating the foundations of
Survival Curve for Cancer Patients Following Treatment
TLDR
A simple function, in terms of two physically meaningful parameters, has been evolved, which fits survivorship data very well and can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics.
Methods of Measuring Useful Life of Equipment under Operational Conditions
TLDR
Methods of estimating relative and absolute longevities are given for the case where k types of equipment are being compared and various logistical requirements are placed upon the replacement policies.
Bibliography of Nonparametric Statistics and Related Topics
Abstract This bibliography contains 999 references on nonparametric statistics and related topics, classified as follows: (A) Surveys and Discussions (39), (B) Theory (31), (C) Tchebycheff
AN ANALYSIS OF SOME FAILURE DATA
TLDR
The rationale and statistical techniques employed in the analysis of some failure data obtained from operations performed by machines and people are summarized and the agreement between theory and data is evaluated.
The standard error of an estimate of expectation of life, with special reference to expectation of tumourless life in experiments with mice
An expectation of life limited to n years is properly defined by to which the approximation usually used is
XXVII. On the statistical estimation of mean life-times
Abstract Statistical methods of estimation of the mean life-times of unstable particles from cloud chamber photographs are discussed (i) for decaying particles only, (ii) when non-decaying particles
...
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