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|a (JST)2674059
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|a eng
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|a Kochar, Subhash C.
|e verfasserin
|4 aut
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|a Estimation of a Monotone Mean Residual Life
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|c 2000
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|a In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x, M(x), defined by $M(x) = E[X-x\mid X > x]$ , where X is a lifetime. M is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of M and their properties. Although tests for a monotone M are discussed in the literature, we are not aware of any estimators of M under these order restrictions. In this paper we initiate a study of such estimation. Our projection type estimators are shown to be strongly uniformly consistent on compact intervals, and they are shown to be asymptotically "root-n" equivalent in probability to the (unrestricted) empirical estimator when M is strictly monotone. Thus the monotonicity is obtained "free of charge", at least in the aymptotic sense. We also consider the nonparametric maximum likelihood estimators. They do not exist for the IMRL case. They do exist for the DMRL case, but we have found the solutions to be too complex to be evaluated efficiently.
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|a Copyright 2000 Institute of Mathematical Statistics
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|a Mean Residual Life
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|a Order Restricted Inference
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|a Asymptotic Theory
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Inferential statistics
|x Statistical estimation
|x Estimation methods
|x Estimators
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|a Mathematics
|x Applied mathematics
|x Analytics
|x Analytical estimating
|x Maximum likelihood estimation
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Inferential statistics
|x Statistical estimation
|x Estimation methods
|x Estimators
|x Consistent estimators
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|x Continuous probability distributions
|x Density distributions
|x Reliability functions
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Inferential statistics
|x Statistical estimation
|x Estimation methods
|x Estimators
|x Maximum likelihood estimators
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|a Social sciences
|x Communications
|x Censorship
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|a Mathematics
|x Applied mathematics
|x Analytics
|x Analytical estimating
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Actuarial science
|x Actuarial cost methods
|x Life tables
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|a Health sciences
|x Medical sciences
|x Pharmacology
|x Clinical pharmacology
|x Pharmacokinetics
|x Dosage
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Euclidean geometry
|x Geometric lines
|x Line segments
|x Estimation under Constraints
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|a research-article
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|a Mukerjee, Hari
|e verfasserin
|4 aut
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|a Samaniego, Francisco J.
|e verfasserin
|4 aut
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|i Enthalten in
|t The Annals of Statistics
|d Institute of Mathematical Statistics
|g 28(2000), 3, Seite 905-921
|w (DE-627)270129162
|w (DE-600)1476670-X
|x 00905364
|7 nnns
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|g volume:28
|g year:2000
|g number:3
|g pages:905-921
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|u https://www.jstor.org/stable/2674059
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|d 28
|j 2000
|e 3
|h 905-921
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