umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Subset selection based on likelihood from uniform and related populations
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1979 (English)Report (Other academic)
Abstract [en]

Let π1,  π2, ... π be k (>_2) populations. Let  πi (i = 1, 2, ..., k) be characterized by the uniform distributionon (ai, bi), where exactly one of ai and bi is unknown. With unequal sample sizes, suppose that we wish to select arandom-size subset of the populations containing the one withthe smallest value of 0i = bi - ai. Rule Ri selects πi iff a likelihood-based k-dimensional confidence region for the unknown (01,..., 0k) contains at least one point having 0i as its smallest component. A second rule, R, is derived through a likelihood ratio and is equivalent to that of Barr and Rizvi (1966) when the sample sizes are equal. Numerical comparisons are made. The results apply to the larger class of densities g(z; 0i) = M(z)Q(0i) iff a(0i) < z < b(0i). Extensions to the cases when both ai and bi are unknown and when 0max is of interest are i i indicated.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1979. , 28 p.
Series
Statistical research report, ISSN 0348-0399 ; 7
Keyword [en]
Subset selection, likelihood ratio, order restrictions, uniform distribution
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-74924OAI: oai:DiVA.org:umu-74924DiVA: diva2:634887
Projects
digitalisering@umu
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

Open Access in DiVA

Subset selection based on likelihood from uniform and related populations(3085 kB)63 downloads
File information
File name FULLTEXT02.pdfFile size 3085 kBChecksum SHA-512
cd3eccbb73f6f6645e97924019d5a67f212ea1ac14c271daf446c6a607527e516fb31d22b828fe84cb94bd6bd8069bdefb4eb6510a5c369e76d709d042216859
Type fulltextMimetype application/pdf

Authority records BETA

Chotai, Jayanti

Search in DiVA

By author/editor
Chotai, Jayanti
By organisation
Mathematical statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 63 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 51 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf