Proper bayes minimax estimators for a multivariate normal mean with unknown common variance under a convex loss function

Autor:	Amany Mousa, Pi-Erh Lin
Rok vydání:	1982
Předmět:	Statistics and Probability Combinatorics Bayes' theorem Bayes estimator Generalization Diagonal matrix Statistics Regular polygon Multivariate normal distribution Function (mathematics) Minimax estimator Mathematics
Zdroj:	Annals of the Institute of Statistical Mathematics. 34:441-456
ISSN:	1572-9052 0020-3157
DOI:	10.1007/bf02481043
Popis:	Let X ∼ Np(µ,σ2Ip) and let s/σ2 ∼ χ n 2 , independent ofX, where μ and σ2 are unknown. This paper considers the estimation of μ (by δ) relative to a convex loss function given by (δ−µ)′[(1−α)Ip/σ2+αQ](δ−µ)/[(1−α)p/σ2+α tr (Q)], whereQ is a knownp×p diagonal matrix and 0≦α≦1. Two classes of minimax estimators are obtained for μ whenp≦3; the first is a new result and the second is a generalization of a result of Strawderman (1973,Ann. Statist.,1, 1189–1194). A proper Bayes estimator is also obtained which is shown to satisfy the conditions of the second class of minimax estimators. The paper concludes by discussing the estimation of μ relative to another convex loss function.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3d919f156ce820ebacfb748c83696cf3 https://doi.org/10.1007/bf02481043 Zobrazit plný text záznamu Full text from SpringerLink