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- W2000989994 abstract "A nonparametric solution is given for the problem of selecting a subset of $k$ populations which with high probability contains the one with the largest $alpha$-quantile, $0 < alpha < 1$. It is assumed that each population has associated with it a continuous cdf $F_i(x) (i = 1, 2, cdots, k)$, that samples of equal sizes are taken from each population and that observations from the same or different populations are all independent. We use the notation of the companion paper [7] without redefining all the symbols and, in particular, it is convenient to identify each population by its cdf. A procedure for the problem, based on order statistics is proposed in Section 2 and limitations on its feasibility in terms of a bound $P_1$ on the possible guarantee probability $P^ast$ are examined in Section 3. An asymptotic expression in terms of tabled functions is also given for $P_1$. The expected size of the selected subset is examined exactly in Section 4 and asymptotically in Section 5; the latter also contains an asymptotic formula for the smallest sample size $n$ required to meet the $P^ast$-guarantee. Asymptotic relative efficiency evaluations of the proposed procedure are carried out in Section 5. Section 6 treats the dual problem of selecting the smallest $alpha$-quantile; Section 7 verifies a monotonicity property. Extensive tables giving $P_1$ and the integer constant defining the procedure are provided for the case $alpha = frac{1}{2}$." @default.
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- W2000989994 date "1967-12-01" @default.
- W2000989994 modified "2023-09-30" @default.
- W2000989994 title "Nonparametric Procedures for Selecting A Subset Containing the Population with the Largest $alpha$-Quantile" @default.
- W2000989994 doi "https://doi.org/10.1214/aoms/1177698612" @default.
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