Summary
In multiparameter estimation for multivariate discrete distributions with infinite support, inadmissibility problems in situations where the multivariate probability distribution function isnot a product of the one-dimensional marginal probability distribution functions have previously been unexplored. This paper examines the inadmissibility problem in some of these situations. Special attention is given to estimating the mean of a negative multinomial distribution. In estimating the mean vector, certain Clevenson-Zidek type estimators are shown to be uniformly better than the usual estimator under a large class of generally scaled squared loss functions. Some of the results are generalized to other multivariate discrete distributions and to situations where several independent negative multinomial distributions are considered.
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Tsui, KW. Multiparameter estimation for some multivariate discrete distributions with possibly dependent components. Ann Inst Stat Math 38, 45–56 (1986). https://doi.org/10.1007/BF02482499
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DOI: https://doi.org/10.1007/BF02482499