Minimax subset selection for the multinomial distribution

Roger L. Berger

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let (X1,...,Xk) be a multinomial vector with unknown cell probabilities (p1,⋯,pk). A subset of the cells is to be selected in a way so that the cell associated with the smallest cell probability is included in the selected subset with a preassigned probability, P*. Suppose the loss is measured by the size of the selected subset, S. Using linear programming techniques, selection rules can be constructed which are minimax with respect to S in the class of rules which satisfy the P*-condition. In some situations, the rule constructed by this method is the rule proposed by Nagel (1970). Similar techniques also work for selection in terms of the largest cell probability.

Original languageEnglish (US)
Pages (from-to)391-402
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume4
Issue number4
DOIs
StatePublished - 1980
Externally publishedYes

Fingerprint

Multinomial Distribution
Subset Selection
Minimax
Cell
Set theory
Subset
Linear programming
Selection Rules
Unknown

Keywords

  • Expected Subset Size
  • Linear Programming
  • Minimax Subset Selection

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Minimax subset selection for the multinomial distribution. / Berger, Roger L.

In: Journal of Statistical Planning and Inference, Vol. 4, No. 4, 1980, p. 391-402.

Research output: Contribution to journalArticle

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