Testing Multiparameter Hypotheses
Let the distribution of some random variables depend on real parameters θ1, • • •, θs and consider the hypothesis H: θi ≦ θi*, i = 1, • • •,s. It is shown under certain regularity assumptions that unbiased tests of H do not exist. Tests of minimum bias and other types of minimax tests are derived under suitable monotonicity conditions. Certain related multidecision problems are discussed and two-sided hypotheses are considered very briefly.