## Abstract

Let (X_{1},...,X_{k}) be a multinomial vector with unknown cell probabilities (p_{1},⋯,p_{k}). 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 language | English (US) |
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Pages (from-to) | 391-402 |

Number of pages | 12 |

Journal | Journal of Statistical Planning and Inference |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - 1980 |

## Keywords

- Expected Subset Size
- Linear Programming
- Minimax Subset Selection

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics