Annals of Statistics
For a given family F of continuous cdf's n i.i.d. random variables with cdf F∈F are observed sequentially with the object of choosing the largest. An upper bound for the greatest asymptotic probability of choosing the largest is α≐.58, the optimal asymptotic value when F is known, and a lower bound is e−1, the optimal value when the choice is based on ranks. It is known that if F is the family of all normal distributions a minimax stopping rule gives asymptotic probability α of choosing the largest while if F is the family of all uniform distributions a minimax rule gives asymptotic value e−1. This note considers a case intermediate to these extremes.
Petruccelli, J. D. (1980). On a Best Choice Problem with Partial Information. Annals of Statistics, 8(5), 1171-1174. http://dx.doi.org/10.1214/aos/1176345156
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