# Accession Number:

## ADA099613

# Title:

## On the Problem of Finding a Best Population with Respect to a Control in Two Stages,

# Descriptive Note:

# Corporate Author:

## PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1981-03-01

# Pagination or Media Count:

## 29.0

# Abstract:

Let pi1,..., pik be given populations associated with unknown real parameters thetal,...,thetai is assumed to be good if thetai thetaO, where thetaO epsilon R is a given control value, i 1,...,k. The goal is to find the best population i.e. that one with the largest parameter, if it is good, in 2 stages with screening out bad populations in the first stage. Consideration is restricted to permutation invariant procedures. It is shown that under MLR and a general invariant loss structure the natural final decisions are optimum. More generally an extension of the Bahadur-Goodman Theorem to sequential settings with and without relation to a control is derived. If the loss structure consists of the cost for sampling plus the loss for final decision, it is shown that for every symmetric prior there exists a Bayes procedure which selects at the first stage populations according to the largest observations. Natural procedures, which screen out with the UMP test for H theta thetaO versus K theta thetaO at fixed level alpha, are considered. As an example, all results are studied in the special case of normal populations with unknown means and a common known variance. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability