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Simultaneous Tests of Hypothesis & confidence Intervals

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Title Simultaneous Tests of Hypothesis & confidence Intervals
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Creator M.C. Verma
 
Subject quasi-independent tests
additive loss functions
 
Description Not Available
Simultaneous tests of significance are of very common occurrence especially in the Analysis of Variance. For performing such tests many times orthogonality of the estimates corresponding to the hypotheses is demanded. But this being insufficient for the criterion of independent of various tests, which itself is too strict, another notion of quasi-independence is presented. In many situations where orthogonality is an exception rather than, a rule, such quasi-independent tests can still be constructed and have been presented by Ghosh (1955). In carrying out such tests simultaneously on the same data we may consider only the individual levels of significance if the decisions are more or less unrelated. In the other case we have to combine such levels of significance in some meaningful way. One of these methods is based on the notion of simultaneous level of significance. Several examples have been discussed to show the necessity of using simultaneous level of significance under different conditions.
Treating the tests of several hypotheses in the frame work of multiple-decision theory of statistical decision functions, additive loss functions have been used. For convenience, maximum and Bayes solutions have been obtained for normal distribution. Under certain conditions, the optimum properties of the product decision procedure can be derived from these of individual procedures. These conditions are satisfied if we consider quasi-independent tests showing that in such cases quasi-independence is at least as good a criterion for optimality as independence. Continuous loss functions are sought to be used for they are more realistic. Under certain loss strict conditions product procedures for testing the means of a bi-variate normal distribution are obtained and can be generalized for the multivariate case.
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Date 2018-08-24T10:18:53Z
2018-08-24T10:18:53Z
1961-01-01
 
Type Dissertation/Thesis
 
Identifier M.C. Verma (1961) , Simultaneous Tests of Hypothesis & confidence Intervals, Unpublished Diploma in Agricultural and Animal Husbandry Statistics, IASRI, New Delhi
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http://krishi.icar.gov.in/jspui/handle/123456789/6568
 
Language English
 
Relation Not Available;
 
Publisher ICAR-IASRI (Erstwhile IARS), New Delhi