Some Locally Optimal Subset Selection Rules.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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Let pio,pi1,...,pik be k 1 independent populations where pii has the associated density function fx, theta sub i with the unknown parameter belonging to an interval H of the real line. Two types of problems are studied 1 to select from pi1,...,pik those populations, if any, that are better to be suitably defined than pio which is the control population and 2 to select from pi1,...,pik a subset preferably of small size so as to contain the best population. For both problems, some locally optimal selection rules are derived. The optimality criteria employed in the two problems are different. Further, the procedure for the second problem is based on ranks though the densities are assumed to be known but for the values of the parameters. The rule in the first case is applied to the special cases of 1 normal means comparison with common known variance and unequal sample sizes 2 normal means comparison with common unknown variance and unequal sample sizes, and 3 gamma scale parameters comparison with unequal shape parameters. The rank procedure is specialized to the case of logistic distributions. Author
- Statistics and Probability