On Subset Selection Rules with Certain Optimality Properties

摘要

The rejection of the hypothesis that the k tested populations are identically distributed is in most cases not satisfactory enough to the experimenter. What he really wants to know is not whether the populations are different, but which ones are significantly different from the others and how big the deviations are. For the case where all but one are identical an answer was found by Mosteller testing homogeneity against slippage alternatives. The general problem has been approached in two different ways. The first, known as indifferent zone approach, states the goal as selecting the best population with a predetermined guaranteed probability provided that this best one exceeds the others by a preassigned amount in terms of a suitable defined distance function. This formulation is due to Bechhofer. The second, which is the one used in the investigations of the present thesis, is the subset selection approach formulated by Gupta, where the goal is the selection of a subset containing the best population with a preassigned probability. Here the number of populations retained in the selected subset is a random variable. The best population may be the one with highest (lowest) parameter value if the distributions come from a one-parameter family, in general it is the one which precedes the others with respect to some (partial) order relation. (Author)