Abstract
n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p1(x) or p2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.
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