An integrated selection formulation for the best normal mean: the unequal and unknown variance case. Issue 1 (2002) - Chen, Pinyuen
Abstract : 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( P Z ) and the indifference zone( I Z ) . In theP Z we insist on selecting the best for a correct selection( C S 1 ) but in theI Z we define any selected subset to be correct( C S 2 ) if it contains the best population. We find the least favorable configuration( L F C ) and the worst configuration( W C ) respectively inP Z andI Z . We derive formulas forP ( C S 1 | L F C ), P ( C S 2 | W C ) and the bounds for the expected sample sizeE ( N ) . 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.