Selection and ranking procedures based on likelihood ratios

• 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

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Subset selection

likelihood ratio

hypothesis testing

order restrictions

normal distribution

uniform distribution

complete ranking

P* -condition

loss function

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