Mathematical Statistics

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, … , P_a} of populations must be made. These populations correspond with random variables Y_i with distribution functions F(y, θ_i) , i = 1 , … , a, where for each i at least one component θ_ij of is unknown. By a real‐valued score function , the θ_i are mapped into R¹. For independent random samples with positive integer n_i, decisions about the shall be made. We already have statistical tests for this. For instance, in simple analysis of variance model I with N(μ_i, σ²) normally ...