On confidence sequences for the mean vector of a multivariate normal distribution

Rasul A. Khan

Journal of Multivariate Analysis, 1978, vol. 8, issue 4, 550-558

Abstract: Let X1, X2,... be idd random vectors with a multivariate normal distribution N([mu], [Sigma]). A sequence of subsets {Rn(a1, a2,..., an), n >= m} of the space of [mu] is said to be a (1 - [alpha])-level sequence of confidence sets for [mu] if P([mu] [set membership, variant] Rn(X1, X2,..., Xn) for every n >= m) >= 1 - [alpha]. In this note we use the ideas of Robbins Ann. Math. Statist. 41 (1970) to construct confidence sequences for the mean vector [mu] when [Sigma] is either known or unknown. The constructed sequence Rn(X1, X2, ..., Xn) depends on Mahalanobis' or Hotelling's according as [Sigma] is known or unknown. Confidence sequences for the vector-valued parameter in the general linear model are also given.

Keywords: Confidence; sequences; mean; vector; multivariate; normal; distribution; martingale; maximal; invariant; hypergeometric; function (search for similar items in EconPapers)
Date: 1978
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(78)90032-5
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:8:y:1978:i:4:p:550-558

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 ().