### 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) |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Expected Subset Size
- Linear Programming
- Minimax Subset Selection

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Planning and Inference*,

*4*(4), 391-402. https://doi.org/10.1016/0378-3758(80)90024-5

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

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 4, no. 4, pp. 391-402. https://doi.org/10.1016/0378-3758(80)90024-5

}

TY - JOUR

T1 - Minimax subset selection for the multinomial distribution

AU - Berger, Roger L.

PY - 1980

Y1 - 1980

N2 - 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.

AB - 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.

KW - Expected Subset Size

KW - Linear Programming

KW - Minimax Subset Selection

UR - http://www.scopus.com/inward/record.url?scp=49149145542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149145542&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(80)90024-5

DO - 10.1016/0378-3758(80)90024-5

M3 - Article

AN - SCOPUS:49149145542

VL - 4

SP - 391

EP - 402

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 4

ER -