Testing problems with linear or angular inequality constraints
The monograph deals with the problem of testing when the alternative is restricted by linear inequality constraints. The main approach is to replace the linear inequalities by one angular inequality and then to apply the likelihood ratio principle. Implementation requires that a suitable member be selected from the class of available circular likelihood ratio tests (CLR). Chapter 1 introduces the general class of testing problems for which CLR- tests can be constructed. A number of case studies are given. Chapter 2 summarizes the basic results from the literature about likelihood ratio tests and ``linear tests''. Chapter 3 gives some CLR-tests and their critical values. Chapter 4 contains the main results of the monograph. In the normal case, the most stringent CLR-test is determined. Overall power properties of the CLR-tests are discussed. Relevant formulas are given for several well-known problems, so that the CLR-tests can be easily constructed. Chapter 5 gives various applications, including one-sided treatment comparisons in two-period cross-over trials with binary outcomes, test expectancy in educational psychology and predatory behavior of hungry beetles. Tables of critical values of certain CLR-tests are given in the Appendix. A substantial list of references is provided in the monograph.
two-period cross-over trials with binary outcomes
scientific article; zbMATH DE number 45775