Summary
The product limit estimator\(\hat F\) of an unknown distributionF is represented as aU-statistic plus an error of the ordero(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0,M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0,M], to the mean life time of an individual up to that time pointM. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.
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Research supported in part by NSA Grant MDA 904-90-H-1001 and by NSF Grant DMS-9007717
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Babu, G.J. Asymptotic theory for estimators under random censorship. Probab. Th. Rel. Fields 90, 275–290 (1991). https://doi.org/10.1007/BF01192165
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DOI: https://doi.org/10.1007/BF01192165
Keywords
- Normal Distribution
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Life Time