Download e-book for iPad: A festschrift for Herman Rubin by Dasgupta A. (ed.)

By Dasgupta A. (ed.)

ISBN-10: 0940600617

ISBN-13: 9780940600614

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1958). Admissibility for estimation with quadratic loss. Ann. Math. Statist. 29, 406–436. MR124101 [19] Lai, W. (1996). Admissibility and the recurrence of Markov chains with applications. D. Thesis, University of Minnesota. [20] Lamperti, J. (1960). Criteria for the recurrence or transience of stochastic processes I. Journal of Math. Anal. Appl. 1, 314–330. MR126872 [21] Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. New York: Springer-Verlag. MR1287609 [22] Revuz, D.

In this case Casella and Strawderman (1981) and Zinzius (1981) showed that the unique minimax estimator of the mean θ for a restriction of the form θ ∈ [−m, m] is the Bayes estimator corresponding to a 2 point prior on {−m, m} for m sufficiently small. The material in section 6 deals with this result, and the large related literature that has followed. In many problems, as in the previous paragraph, Bayes or Generalized Bayes estimators are known to form a complete class. When loss is quadratic and the prior (and hence typically the posterior) distribution is not degenerate at a point, the Bayes estimator cannot take values on the boundary of the parameter space.

K; with θ1 ≤ θ2 ≤ . . ≤ θk , Sackrowitz and Strawderman (1974) investigated the admissibility (for various loss functions) of the MLE of (θ1 , . . , θk ), while Sackrowitz (1982) provided improvements (under sum of squared error losses) to the MLE in the cases above where it is inadmissible. Further examples consist of a series of papers by Shao and Strawderman (1994,1996a,1996b) where, in various models, improvements under squared error loss to truncated estimators are obtained. Further related historical developments are given in the review paper of van Eeden (1996).

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A festschrift for Herman Rubin by Dasgupta A. (ed.)

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