Abstract
We study a class of selection problems for which the 'more sampling-more information' principle is true, but not obvious. The case examined, which includes sampling from a multinomial distribution and from a hypergeometric distribution as special cases, concerns a one-sample procedure to select an m-subset of thef largest denominations in a multivariate Polya urn. For a given sample size n, the selection procedure takes the m denominations with highest frequencies, where ties are broken by randomization. Let +(n) be the probability of making a correct selection when n is the sample size. According to the 'more sampling-more information' principle, we expect 0(n + 1) > 0(n) for all n > 0. This inequality is proved.
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