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Subset selection based on likelihood ratios: the normal means case
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1979 (English)Report (Other academic)
Abstract [en]

Let π1, ..., πk be k(>_2) populations such that πi, i = 1, 2, ..., k, is characterized by the normal distribution with unknown mean and ui variance aio2 , where ai is known and o2 may be unknown. Suppose that on the basis of independent samples of size ni from π (i=1,2,...,k), we are interested in selecting a random-size subset of the given populations which hopefully contains the population with the largest mean.Based on likelihood ratios, several new procedures for this problem are derived in this report. Some of these procedures are compared with the classical procedure of Gupta (1956,1965) and are shown to be better in certain respects.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1979. , 70 p.
Series
Statistical research report, ISSN 0348-0399 ; 6
Keyword [en]
Subset selection, likelihood ratio, order restrictions, loss function, normal distribution
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-74925OAI: oai:DiVA.org:umu-74925DiVA: diva2:634891
Projects
digitalisering@umu
Note

Ny rev. utg.

This is a slightly revised version of Statistical Research Report No. 1978-6.

Available from: 2013-07-02 Created: 2013-07-02 Last updated: 2013-07-02Bibliographically approved
In thesis
1. Selection and ranking procedures based on likelihood ratios
Open this publication in new window or tab >>Selection and ranking procedures based on likelihood ratios
1979 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with random-size subset selection and ranking procedures• • • )|(derived through likelihood ratios, mainly in terms of the P -approach.Let IT , . .. , IT, be k(> 2) populations such that IR.(i = l, . . . , k) hasJ_ K. — 12the normal distribution with unknwon mean 0. and variance a.a , where a.i i i2 . . is known and a may be unknown; and that a random sample of size n^ istaken from . To begin with, we give procedure (with tables) whichselects IT. if sup L(0;x) >c SUD L(0;X), where SÎ is the parameter space1for 0 = (0-^, 0^) ; where (with c: ß) is the set of all 0 with0. = max 0.; where L(*;x) is the likelihood function based on the total1sample; and where c is the largest constant that makes the rule satisfy theP*-condition. Then, we consider other likelihood ratios, with intuitivelyreasonable subspaces of ß, and derive several new rules. Comparisons amongsome of these rules and rule R of Gupta (1956, 1965) are made using differentcriteria; numerical for k=3, and a Monte-Carlo study for k=10.For the case when the populations have the uniform (0,0^) distributions,and we have unequal sample sizes, we consider selection for the populationwith min 0.. Comparisons with Barr and Rizvi (1966) are made. Generalizai<j<k Jtions are given.Rule R^ is generalized to densities satisfying some reasonable assumptions(mainly unimodality of the likelihood, and monotonicity of the likelihoodratio). An exponential class is considered, and the results are exemplifiedby the gamma density and the Laplace density. Extensions and generalizationsto cover the selection of the t best populations (using various requirements)are given. Finally, a discussion oil the complete ranking problem,and on the relation between subset selection based on likelihood ratios andstatistical inference under order restrictions, is given.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 1979. 24 p.
Keyword
Subset selection, likelihood ratio, hypothesis testing, order restrictions, normal distribution, uniform distribution, complete ranking, P* -condition, loss function
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-73690 (URN)
Public defence
1979-06-01, Samhällsvetarhuset, hörsal D, Umeå universitet, Umeå, 09:15
Projects
digitalisering@umu
Available from: 2013-06-26 Created: 2013-06-26 Last updated: 2013-07-02Bibliographically approved

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