11Multiple Decision Problems
A multiple decision problem is given if a decision function can take on two or more values. A good overview about this is given in Gupta and Huang (1981). In this chapter, mainly the case of more than two decisions is discussed, we then speak about true multiple decision problems. Two‐decision problems occur only in special cases (for a = 2). Statistical tests as typical statistical two‐decision problems have a decision function with ‘values’ acceptation of H0 and rejection of H0.
In this chapter we assume that statements about a ≥ 2 populations (distributions) from a set G = {P1, … , Pa} of populations must be made. These populations correspond with random variables Yi with distribution functions F(y, θi) , i = 1 , … , a, where for each i at least one component θij of
is unknown. By a real‐valued score function
, the θi are mapped into R1. For independent random samples
with positive integer ni, decisions about the
shall be made. We already have statistical tests for this. For instance, in simple analysis of variance model I with N(μi, σ2) normally ...