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45 (2004) 21–44 c Institute of Mathematical Statistics, 2004 Estimation in restricted parameter spaces: A review Eric Marchand∗1 and William E. Strawderman2 University of New Brunswick Rutgers University Abstract: In this review of estimation problems in restricted parameter spaces, we focus through a series of illustrations on a number of methods that have proven to be successful. These methods relate to the decision-theoretic aspects of admissibility and minimaxity, as well as to the determination of dominating estimators of inadmissible procedures obtained for instance from the criteria of unbiasedness, maximum likelihood, or minimum risk equivariance.
Sacks, 1963) under squared error loss. Despite the age of this finding, it was not until the paper of Shao and Strawderman (1996a) that explicit improvements were obtained (under squared error loss), and there still remains the open question of finding admissible improvements. As well, Katz’s (1961) uniform Generalized Bayes estimator remains (to our knowledge) the only known minimax and admissible estimator of θ (under squared error loss). 5. Estimating parameters with additional information In this section, we present a class of interesting estimation problems which can be transformed to capitalize on standard solutions for estimation problems in constrained parameter spaces.
Ann. Math. Statist. 76, 518–522. MR70929  Stein, C. (1959). The admissibility of Pitman’s estimator of a single location parameter. Ann. Math. , 30, 970–979. MR109392  Zidek, J. V. (1970). Sufficient conditions for admissibility under squared error loss of formal Bayes estimators. Ann. Math. Statist. 41, 446–456. MR261742 A Festschrift for Herman Rubin Institute of Mathematical Statistics Lecture Notes – Monograph Series Vol. 45 (2004) 21–44 c Institute of Mathematical Statistics, 2004 Estimation in restricted parameter spaces: A review Eric Marchand∗1 and William E.