On the least favorable configuration in mult1hgmial selection problems

1986 ◽  
Vol 15 (2) ◽  
pp. 367-385 ◽  
Author(s):  
Pinyuen Chen
Keyword(s):  
Selection Problems ◽  
Favorable Configuration ◽  
Least Favorable Configuration

scholarly journals An integrated selection formulation for the best normal mean: the unequal and unknown variance case

2002 ◽  
Vol 6 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Pinyuen Chen ◽  
Jun-Lue Zhang
Keyword(s):  
Sample Size ◽  
Parameter Space ◽  
Correct Selection ◽  
Indifference Zone ◽  
Unknown Variance ◽  
Normal Mean ◽  
Favorable Configuration ◽  
Preference Zone ◽  
Selected Subset ◽  
Least Favorable Configuration

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 (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best for a correct selection (CS1) but in the IZ we define any selected subset to be correct (CS2) if it contains the best population. We find the least favorable configuration (LFC) and the worst configuration (WC) respectively in PZ and IZ. We derive formulas for P(CS1|LFC), P(CS2|WC) and the bounds for the expected sample size E(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.

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