The Annals of Statistics

Sequential Selection Procedures--A Decision Theoretic Approach

Shanti S. Gupta and Klaus J. Miescke

Full-text: Open access


Let $\pi_1,\cdots, \pi_k$ be given populations which are associated with unknown real parameters $\theta_1,\cdots, \theta_k$ from a common underlying exponential family $\mathscr{F}$. Permutation invariant sequential selection procedures are considered to find good populations (i.e. those which have large parameters), where inferior populations are intended to be screened out at the earlier stages. The natural terminal decisions, i.e. decisions which are made in terms of largest sufficient statistics, are shown to be optimum in terms of the risk, uniformly in $(\theta_1,\cdots, \theta_k)$, under fairly general loss assumptions. Similar results with respect to subset selections within stages are established under the additional assumption that $\mathscr{F}$ is strongly unimodal (i.e. $\log$-concave). The results are derived in the Bayes approach under symmetric priors. Backward induction as well as the concept of decrease in transposition (DT) by Hollander, Proschan and Sethuraman (1977) are the main tools which are used in the proofs.

Article information

Ann. Statist., Volume 12, Number 1 (1984), 336-350.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F07: Ranking and selection
Secondary: 62F05: Asymptotic properties of tests 62F15: Bayesian inference 62L99: None of the above, but in this section

Multiple decision procedures sequential procedures screening procedures selection procedures Bayesian analysis


Gupta, Shanti S.; Miescke, Klaus J. Sequential Selection Procedures--A Decision Theoretic Approach. Ann. Statist. 12 (1984), no. 1, 336--350. doi:10.1214/aos/1176346411.

Export citation