Marchand, Éric; Najafabadi, Amir T. Payandeh Bayesian improvements of a MRE estimator of a bounded location parameter. (English) Zbl 1271.62046 Electron. J. Stat. 5, 1495-1502 (2011). Summary: We study the frequentist risk performance of Bayesian estimators of a bounded location parameter, and focus on conditions placed on the shape of the prior density guaranteeing dominance over the minimum risk equivariant (MRE) estimator. For a large class of even and logconcave densities, even convex loss functions, we demonstrate in a unified manner that symmetric priors which are bowled shaped and logconcave lead to Bayesian dominating estimators. The results generalize similar results obtained by E. Marchand and W. E. Strawderman [Ann. Inst. Stat. Math. 57, No. 1, 129–143 (2005; Zbl 1082.62029)] for the fully uniform prior, as well as those obtained by T. Kubokawa [Ann. Stat. 22, No. 1, 290–299 (1994; Zbl 0816.62021)] for squared error loss. Finally, we present a detailed example and several remarks. Cited in 4 Documents MSC: 62F15 Bayesian inference 62F10 Point estimation 62F30 Parametric inference under constraints 62C20 Minimax procedures in statistical decision theory Keywords:Bayes estimator; bounded mean; dominance; location family; logconcavity; minimum risk equivariant; restricted parameter space Citations:Zbl 1082.62029; Zbl 0816.62021 × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Gatsonis, C., MacGibbon, B., & Strawderman, W.E. (1987). On the estimation of a restricted normal mean., Statistics & Probability Letters , 6 , 21-30. · Zbl 0647.62015 [2] Hartigan, J.A. (2004). Uniform priors on convex sets improve risk., Statistics & Probability Letters , 67 , 285-288. · Zbl 1041.62021 [3] Kubokawa, T. (1994). A unified approach to improving on equivariant stimators., Annals of Statistics , 22 , 290-299. · Zbl 0816.62021 · doi:10.1214/aos/1176325369 [4] Kubokawa, T. (2005A). Estimation of bounded location and scale parameters., Journal of the Japanese Statistical Society , 35 , 221-249. [5] Kubokawa, T. (2005B). Estimation of a mean of a normal distribution with a bounded coefficient of variation, Sankhyā: The Indian Journal of Statistics , 67 , 499-525. · Zbl 1192.62062 [6] Marchand, É. & Perron, F. (2001). Improving on the MLE of a bounded normal mean., Annals of Statistics , 29 , 1078-1093. · Zbl 1041.62016 · doi:10.1214/aos/1013699994 [7] Marchand, É. & Perron, F. (2005). Improving on the MLE of a bounded mean for spherical distributions., Journal of Multivariate Analysis , 92 , 227-238. · Zbl 1062.62101 · doi:10.1016/j.jmva.2003.09.009 [8] Marchand, É. & Perron, F. (2009). Estimating a bounded parameter for symmetric distributions., Annals of the Institute of Mathematical Statistics , 61 , 215-234. · Zbl 1294.62038 · doi:10.1007/s10463-007-0132-6 [9] Marchand, É., Ouassou, I., Payandeh, A.T. & Perron, F. (2008). On the estimation of a restricted location parameter for symmetric distributions., Journal of the Japanese Statistical Society , 38 , 293-309. [10] Marchand, É. & Strawderman, W.E. (2004). Estimation in restricted parameter spaces: A review., Festschrift for Herman Rubin , IMS Lecture Notes-Monograph Series, 45 , pp. 21-44. · Zbl 1268.62030 · doi:10.1214/lnms/1196285377 [11] Marchand, É. & Strawderman, W.E. (2005A). Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval., Annals of the Institute of Mathematical Statistics , IMS Lecture Notes-Monograph Series, 57 , 129-143. · Zbl 1082.62029 · doi:10.1007/BF02506883 [12] Marchand, É. & Strawderman, W.E. (2005B). On improving on the minimum risk equivariant estimator of a scale parameter under a lower bound constraint, Journal of Statistical Planning and Inference . 134 , 90-101. · Zbl 1067.62025 · doi:10.1016/j.jspi.2004.04.001 [13] van Eeden, C. (2006)., Restricted parameter space problems . Admissibility and minimaxity properties. Lecture Notes in Statistics, 188 , Springer. · Zbl 1160.62018 · doi:10.1007/978-0-387-48809-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.