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- Chotai, Jayanti, 1948-
(författare)
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Likelihood ratio procedures for subset selection and ranking problems
- 1979
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This report deals with procedures for random-size subset selection fromk(> 2) given populations where the distribution of ir^(i = l, ..., k)has a density f^(x;0^). Let ••• -®[k] denote unknown values ofthe parameters, and let ^[i]» ***'ïï[k] denote the corresponding populations.First, we have considered the problem of selection for consider the/sprocedure that selects TT. if sup L(0;x) > c L(0;x), where L(*;x) is the1 e e u . - - - - -itotal likelihood function, where is the region m the parameter space foriA9= (0^, ..., 0^) having 0^ as the largest component, where 9 is the maximum likelihood estimate of 0 , and where c is a given constant with 0 < c < l .With the densities satisfying seme reasonable requirements given in this report,we have shown that for each i, the probability of includingthe selected subset is decreasing in ®[j] f°r j t i anc* increasing inWe have then derived some results on selection for the t(> 1) best populations,thereby generalizing the results for t = 1. For this problem, we haveconsidered a) selection of a set whose elements consist of subsets of thegiven populations having t members, and requiring that the set of the t• » • • •best populations is included with probability at least P , b) selection ofa subset of the populations so as to include all the t best populationswith probability at least P'*, and c) selection of a subset of the populationssuch that TT[j ^ is included with probability at least P*, j=k-t+l,.•., k. In the final section, we have discussed the relation between thetheories of subset selection based on likelihood ratios and statistical inferenceunder order restrictions, and have considered the complete rankingproblem.
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- Chotai, Jayanti, 1948-
(författare)
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Selection and ranking procedures based on likelihood ratios
- 1979
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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
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- Chotai, Jayanti, 1948-
(författare)
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Subset selection based on likelihood from uniform and related populations
- 1979
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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- Chotai, Jayanti, 1948-
(författare)
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Subset selection based on likelihood ratios : the normal means case
- 1979
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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- Edvardsson, Bo, 1944-, et al.
(författare)
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A method for evaluation of metric properties of response scales
- 1973
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- To permit certain statistical operations verbal response categories in questionnaire response scales must be given appropriate numbers. In this study the routines used to assign such numbers are discussed. A method to evaluate the metric properties of response scales, simultaneously being an alternative way of assigning proper numbers, is proposed. For this method, based on subjective estimation, two criteria related to commonality of meaning are suggested. Finally the method is demonstrated in an empirical study on eight different response scales.
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