# Asymptotic comparison of two-stage selection procedures under quasi-Bayesian framework

## TL;DR

This paper analyzes two-stage selection procedures for Gaussian populations, confirming a conjecture about their asymptotic efficiency using a quasi-Bayesian framework and exploring open questions on Student-t maxima.

## Contribution

It introduces a quasi-Bayesian model validating a conjecture on the asymptotic efficiency of selection procedures and discusses open problems on Student-t distribution maxima.

## Key findings

- Conjecture on asymptotic efficiency ratio is validated under the quasi-Bayesian model.
- Provides insights into the extreme value distribution of Student-t maxima.
- Highlights open questions in the theory of Student-t maxima.

## Abstract

This paper revisits the procedures suggested by Dudewicz and Dalal (1975) and Rinott (1978) which are designed for selecting the population with the highest mean among independent Gaussian populations with unknown and possibly different variances. In a previous paper Jacobovic and Zuk (2017) made a conjecture that the relative asymptotic efficiency of these procedures equals to the ratio of two certain sequences. This work suggests a quasi-Bayesian modelling of the problem under which this conjecture is valid. In addition, this paper motivates an open question regarding the extreme value distribution of the maxima of triangular array of independent student-t random variables with an increasing number of degrees of freedom.