Randomized Play-the-Leader Rules for Sequential Sampling from Two Populations

Abstract

Observations may be taken from one of the two populations. A randomized selection rule is one that chooses the populations according to some determined odds. The odds for choosing a population the next time may be dependent on all the observations taken so far from both populations. In this paper, the odds are made for the randomized selection rule in such a way that the number of observations from the better population relative to the number of observations from the other population grows at prescribed rates, typically of exponential order or faster. The rules include randomized play-the-winner rules and randomized analogues of Robbins' R̄ rules. Some Monte Carlo investigations are conducted to study these randomized selection rules for moderate sample sizes.