Two Choice Optimal Stopping∗†
نویسندگان
چکیده
Let Xn, . . . , X1 be i.i.d. random variables with distribution function F . A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V 2 n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence V 2 n for a large class of F ’s belonging to the domain of attraction (for the minimum) D(Gα), where Gα(x) = [1 − exp(−xα)]I(x ≥ 0). The results are compared with those for the asymptotic behavior of the classical one choice value sequence V 1 n , as well as with the “prophet value” sequence V p n = E(min{Xn, . . . , X1}).
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