### Abstract

In a multinomial setting with a fixed number k of cells, the problem of screening out cells to find the “best” cell, i.e., the one with the smallest cell probability, or looking for a (small) subset of cells containing the best cell is revisited. An inverse sampling procedure is used, unlike past work on this problem ([1], [2], [3], and [4]). Finding the cell with the smallest cell probability is clearly more difficult than finding the one with the largest cell probability. The proposed procedure takes one observation at a time (as usual) and assigns a zero to all those (and only those) k — 1 cells into which the observation does not fall Sampling continues sequentially and stops as soon as any one cell has accumulated r zeros. For any given integer c (with 0 ≤ c < r), we put into the selected subset (SS) all those cells with at least r — c zeros and assert that this selected subset contains the best cell. It is important to note that for the slippage configuration (SC) we can attain any specified lower bound P for the probability P(SCB) that the SS contains the best cell by increasing r and need not increase the value of c. Of principal interest is the case c = 0.

Original language | English (US) |
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Pages (from-to) | 117-200 |

Number of pages | 84 |

Journal | Sequential Analysis |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1994 |

### Keywords

- inverse sampling procedure
- least favorable configuration
- multinomial distribution
- selecting a subset containing the best cell
- slippage configuration

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation

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## Cite this

*Sequential Analysis*,

*13*(3), 117-200. https://doi.org/10.1080/07474949408836303