On least squares estimation for categorical data |
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Authors: | Robert P. Clickner |
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Affiliation: | Temple University , Philadelphia, Pennsylvania |
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Abstract: | We consider a multinomial distribution in which the cell probabilities are known arbitrary functions of a vector parameter θ. It is desired to estimate θ by least squares. Three variations of the least squares approach are investigated, and each is found to be equivalent, in the very strong sense of being algebraically identical, to one of the following estimation procedures: maximum likelihood, minimum χ2 and minimum modified χ2. Two of these results also apply to the multiple hypergeometric distribution. |
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Keywords: | equivalence of estimators multinomial distribution, estimation of minimum chi-square estimation maximum likelihood estimation |
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