Title: On The Asymptotic Efficiency of Selection Procedures for Independent Gaussian Populations,
Abstract: The field of discrete event simulation and optimization techniques motivates
researchers to adjust classic ranking and selection (R&S) procedures to the
settings where the number of populations is large. We use insights from extreme
value theory in order to reveal the asymptotic properties of R&S procedures.
Namely, we generalize the asymptotic result of Robbins and Siegmund regarding
selection from independent Gaussian populations with known constant variance by
their means to the case of selecting a subset of varying size out of a given
set of populations. In addition, we revisit the problem of selecting the
population with the highest mean among independent Gaussian populations with
unknown and possibly different variances. Particularly, we derive the relative
asymptotic efficiency of Dudewicz and Dalal's and Rinott's procedures, showing
that the former can be asymptotically superior by a multiplicative factor which
is larger than one, but this factor may be reduced by proper choice of
parameters. We also use our asymptotic results to suggest that the sample size
in the first stage of the two procedures should be logarithmic in the number of
populations.