An integrated selection formulation for the best normal mean: the unequal and unknown variance case
This paper considers an integrated formulation in selecting the best normal mean in the case of unequal and unknown variances. The formulation separates the parameter space into two disjoint parts, the preference zone and the indifference zone . In the we insist on selecting the best for a correct selection but in the we define any selected subset to be correct if it contains the best population. We find the least favorable configuration and the worst configuration respectively in and . We derive formulas for , and the bounds for the expected sample size . We also give tables for the procedure parameters to implement the proposed procedure. An example is given to illustrate how to apply the procedure and how to use the table.