Estimation in restricted parameter spaces: a review. (English) Zbl 1268.62030

Dasgupta, Anirban (ed.), A Festschrift for Herman Rubin. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-61-7/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 45, 21-44 (2004).
Summary: 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. Finally, we accompany the presentation of these methods with various related historical developments.
For the entire collection see [Zbl 1066.62002].


62F10 Point estimation
62F30 Parametric inference under constraints
62C15 Admissibility in statistical decision theory
62C20 Minimax procedures in statistical decision theory