Biases of the maximum likelihood and Cohen-Sackrowitz estimators for the tree-order model

Sanjay Chaudhuri and Michael D. Perlman

Statistics & Probability Letters, 2005, vol. 71, issue 3, 267-276

Abstract: Consider s+1 univariate normal populations with common variance [sigma]2 and means [mu]i, i=0,1,...,s, constrained by the tree-order restrictions [mu]i[greater-or-equal, slanted][mu]0, i=1,2,...,s. For certain sequences [mu]0,[mu]1,... the maximum likelihood-based estimator (MLBE) of [mu]0 diverges to -[infinity] as s-->[infinity] and its bias is unbounded. By contrast, the bias of an alternative estimator of [mu]0 proposed by Cohen and Sackrowitz (J. Statist. Plan. Infer. 107 (2002) 89-101) remains bounded. In this note the biases of the MLBEs of the other components [mu]1,[mu]2,... are studied and compared to the biases of the corresponding Cohen-Sackrowitz estimators (CSE). Unlike the MLBE of [mu]0, the MLBEs of [mu]i for i[greater-or-equal, slanted]1, are asymptotically unbiased in most cases. By contrast, the CSEs of [mu]i, i=1,2,...,s more often have nonzero asymptotic bias.

Keywords: Order-restricted; inference; Tree; order; Maximum; likelihood; estimator; Cohen-Sackrowitz; estimator; Bias (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00308-6
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:stapro:v:71:y:2005:i:3:p:267-276

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

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().