Robbins' problem of optimal stopping asks one to minimise the expected { \it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the { \it value} of the stopped variable under the rule optimal in the sense of the rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.
Categories: math.PR