For a given family $\mathscr{F}$ of continuous cdf's $n$ i.i.d. random variables with cdf $F \in \mathscr{F}$ are observed sequentially with the object of choosing the largest. An upper bound for the greatest asymptotic probability of choosing the largest is $\alpha \doteq .58,$ 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 $\mathscr{F}$ is the family of all normal distributions a minimax stopping rule gives asymptotic probability $\alpha$ of choosing the largest while if $\mathscr{F}$ is the family of all uniform distributions a minimax rule gives asymptotic value $e^{-1}.$ This note considers a case intermediate to these extremes.
@article{1176345156,
author = {Petruccelli, Joseph D.},
title = {On a Best Choice Problem with Partial Information},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 1171-1174},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345156}
}
Petruccelli, Joseph D. On a Best Choice Problem with Partial Information. Ann. Statist., Tome 8 (1980) no. 1, pp. 1171-1174. http://gdmltest.u-ga.fr/item/1176345156/