Minimax estimators of the multinormal mean: Autoregressive priors

L. R. Haff

Journal of Multivariate Analysis, 1976, vol. 6, issue 2, 265-280

Abstract: Empirical Bayes estimators are given for the mean of a k-dimensional normal distribution, k >= 3. We assume that y ~ Nk([theta], V1), V1 = diag(vi), vi known (i = 1, 2,..., k); also, [theta] ~ Nk(0, V2) - V2 defined by one or more unknown parameters. Of particular interest is V2 generated by an autoregressive process. A recent result of Efron and Morris is used to obtain necessary and sufficient conditions for the minimaxity of our estimators. Practical sufficient conditions (for minimaxity) are obtained by exploiting the structure of V2. Another result shows that our estimators have good Bayesian properties. Estimates of the exact size of Pearson's chi-square test are given in an example; the autoregressive prior is very natural in this situation.

Keywords: Autoregressive; prior; empirical; Bayes; Stein-like; estimators; minimax; extended; Bayes (search for similar items in EconPapers)
Date: 1976
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(76)90036-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:6:y:1976:i:2:p:265-280

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().