Hypothesis testing with a restricted parameter space
The paper considers tests of hypothethes in parametric models in which the parameter of interest is restricted under the alternative hypothesis. As examples of hypotheses of this type can be considered multivariate one-sided hypotheses, joint one- and two-sided hypotheses, and multivariate non-negativity hypotheses. The focus of the paper is on the choice and optimality properties of test statistics. The author specifies a weighted average power optimality criterion and derives tests that are optimal or asymptotically optimal according to this criterion. Exact results are established first for Gaussian linear regression models with known variance and for dynamic nonlinear models the analogical asymptotic properties are derived. The theoretical results outlined above are supplemented by simulation results.
scientific article; zbMATH DE number 1124515
scientific article