Subset Selection Toward Optimizing the Best Performance at a Second Stage

In the search for the best of n candidates, two-stage procedures of the following type are in common use. In a first stage, weak candidates are removed, and the subset of promising candidates is then further examined. At a second stage, the best of the candidates in the subset is selected. In this article, optimization is not aimed at the parameter with largest value but rather at the best performance of the selected candidates at Stage 2. Under a normal model, a new procedure based on posterior percentiles is derived using a Bayes approach, where nonsymmetric normal (proper and improper) priors are applied. Comparisons are made with two other procedures frequently used in selection decisions. The three procedures and their performances are illustrated with data from a recent recruitment process at a Midwestern university.     

On (n-l)-wise and joint independence and normality of n Random variables: an example

An example is given of a vector of n random variables such that any (n-1)-dimensional subvector consists of n-1 independent standard normal variables. The whole vector however is neither independent nor normal.     

Bayesian look ahead one stage sampling allocations for selecting the largest normal mean

From two independent normal populations with unknown means and a common known variance, samples of unequal sizes are observed at stage 1. The goal is to find that population with the larger mean. Using the Bayes approach, optimum allocations ofm additional observations, at stage 2, are derived under the linear and the 0–1 loss.     

On a conjecture concerning the least favorable configuration of certain two-stage selection procedures

Given k normal populations with unknown means and a common known variance a two-stage procedure p₁ with screening in the first stage to find the population with the largest mean using the indifference-zone approach is under concern. It was proposed and studied previously by Cohen (1959), Alam (1970) and Tamhane and Bechhofer (1977, 1979). But up to now a conjecture concerning the least favorable parameter configuration of p₁remained unproved for k ≥ 3. In this paper we give a non-standard proof of the conjecture in case of k = 3 for p₁. which (under minor changes) works also for a simplified version of p₁,. Besides, a counterexample is provided to show that another (more intuitive) method of proof fails to work.