Graduate Thesis Or Dissertation
 

Multinomial estimation from censored samples

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/jd473067n

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  • Consider the estimation of the category proportions in a multinomial population from a sample which is "censored" in the sense that under an appropriate, unknown permutation of the sample categories, the population proportions are all known. We are considering the estimation of an ordered set of sample proportions, known except for their order. The estimation problem reduces to one of matching a set of known sample proportions with a set of known population proportions. The method of maximum likelihood yields the matching that common sense or one's intuition would suggest; highest sample proportion associated with highest population proportion, second highest sample proportion with second highest population proportion, and so forth. The work of this thesis is to examine, by a complete enumeration of cases for some simple problems, how good the method of maximum likelihood is. We study the effectiveness of maximum likelihood matching under variation of the three factors (1) "roughness" of the set of population proportions, (2) number of categories of the multinomial population, and (3) size of the sample. The effectiveness of maximum likelihood matching is measured by the ratio "proportion of the time maximum likelihood matching correct" divided by "proportion of the time random matching correct". The empirical study confirms the conclusions suggested by intuition that: (1) the greater the "roughness" of the set of population proportions, the more effective is the method of maximum likelihood; (2) the greater the number of categories the more effective is the method of maximum likelihood; and (3) the greater the sample size the more effective is the method of maximum likelihood.
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