A class of selection problems for which more sampling is more informative
Francis C. Hsuan, F. K. Hwang, Milton N. Parnes · Biometrika · 1982
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 the f 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 ψ(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 ψ(n+1)≥ψ(n) for all n > 0. This inequality is proved.