Selecting among the multinomial losers

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.