Subset selection for the least probable multinomial cell

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Abstract

An inverse sampling procedure R is proposed for selecting a randomsize subset which contains the least probable cell (i.e., the cell with the smallest cell probabilities) from a multinomial distribution with k cells. Type 2-Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the limits of integration, (ii) to prove that the least favorable configuration under R is the so-called slippage configuration with k equal cell probabilities, and (iii) to express exactly the expectation of the total number of observations required and the expectation of the subset size under the procedure R.

Original languageEnglish (US)
Pages (from-to)303-314
Number of pages12
JournalAnnals of the Institute of Statistical Mathematics
Volume37
Issue number1
DOIs
StatePublished - Dec 1 1985

Keywords

  • Dirichlet integral
  • inverse sampling
  • least favorable configuration
  • multinomial distribution
  • subset selection formulation

ASJC Scopus subject areas

  • Statistics and Probability

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