On the Problem of Finding a Best Population with Respect to a Control in Two Stages,
Abstract
Let pi1,..., pi(k) be given populations associated with unknown real parameters theta(l),...,theta(i) is assumed to be 'good' if theta(i) > theta(O), where theta(O) 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 < theta(O) versus K: theta > theta(O) 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1981
- Accession Number
- ADA099613
Entities
People
- Klaus-j. Miescke
- Shanti Gupta
Organizations
- Purdue University