## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 11, Number 2 (2017), 5375-5405.

### On the asymptotic efficiency of selection procedures for independent Gaussian populations

Royi Jacobovic and Or Zuk

#### 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.

#### Article information

**Source**

Electron. J. Statist., Volume 11, Number 2 (2017), 5375-5405.

**Dates**

Received: July 2017

First available in Project Euclid: 28 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1514430422

**Digital Object Identifier**

doi:10.1214/17-EJS1375

**Mathematical Reviews number (MathSciNet)**

MR3743734

**Zentralblatt MATH identifier**

06825050

**Subjects**

Primary: 62F07: Ranking and selection

Secondary: 62L99: None of the above, but in this section

**Keywords**

Selection procedures asymptotic statistics extreme value theory discrete events simulation

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Jacobovic, Royi; Zuk, Or. On the asymptotic efficiency of selection procedures for independent Gaussian populations. Electron. J. Statist. 11 (2017), no. 2, 5375--5405. doi:10.1214/17-EJS1375. https://projecteuclid.org/euclid.ejs/1514430422