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Order statistics and inference. Estimation methods. (English) Zbl 0732.62044
Statistical Modeling and Decision Science. Boston, MA etc.: Academic Press, Inc. xix, 377 p. $ 79.95 (1991).
The book may shortly be described by the subtitle ‘estimation methods’ based on censored samples and a selected number of order statistics. After the presentation of theoretical results, the estimation of location and scale parameters is extensively studied in uniform, logistic, gamma, Weibull, normal, half logistic models etc. The performance of linear estimators, maximum likelihood estimators and modifications thereof is measured with respect to the variance. Hence the book may be regarded as a good reference source for formulas of exact and approximate variances of estimators of that type. Numerical examples illustrate the accuracy of such approximations.
Contents: 1. Introduction. 2. Basic theory. 3. Moments and other expected values. 4. Linear estimation based on order statistics. 5. Maximum likelihood estimation. 6. Approximate maximum likelihood estimation. 7. Optimal linear estimation based on selected order statistics. 8. Cohen- Whitten estimator: using order statistics. 9. Estimation in regression models. 10. A sample completion technique for censored samples.
Reviewer: R.D.Reiß (Siegen)

62G30 Order statistics; empirical distribution functions
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62F10 Point estimation