Selecting Multinomial Populations
Abstract
This paper deals with the problem of selecting fair multinomial populations compared with a standard. The concept of diversity within a population is of considerable importance in statistical theory and applications. The problem of measuring diversity arises in a variety of studies in ecology, sociology, econometrics, genetics and many other sciences. Two selection procedures are investigated: the natural selection procedure of Gupta and Leu (1989) and an empirical Bayes simultaneous selection procedure. It is proved that the natural selection procedure is a Bayes procedure relative to a symmetric Dirichlet prior distribution, and therefore is an admissible selection procedure. For the empirical Bayes simultaneous selection procedure, the associated asymptotic optimality is investigated. It is shown that the proposed empirical Bayes selection procedure is shown to be of order O(exp(-tk+1n k)) for some positive constant t, where k is the number of populations involved in the selection problem. Keywords: Fair multinomial population; Entropy function; Gini-Simpson index; Natural selection procedure; Empirical Bayes selection procedures; Asymptotically optimal; Rate of convergence.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1990
- Accession Number
- ADA219256
Entities
People
- Shanti Gupta
- Tachen Liang
Organizations
- Purdue University