Testing Problems with Linear or Angular Inequality Constraints - Johan C. Akkerboom

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Sommaire:
1 Testing problems with linear inequality constraints.- 1.0 General introduction and outline of results.- 1.1* Notations.- 1.2 Testing statistical hypotheses.- 1.3 Cases from statistical practice.- 1.4 The general problem with the alternative restricted by linear inequalities.- 1.5 The canonical form: testing against the pointed polyhedral cone K.- 1.6 Particular classes of testing problems with the alternative restricted by linear inequalities.- 1.7 Problems with the null hypothesis restricted by linear inequalities.- 2 The main problem: testing against the pointed polyhedral cone K.- 2.0 Introduction and summary.- 2.1* Linear inequality constraints and the geometry of polyhedral cones.- 2.2 Linear tests.- 2.3 Likelihood ratio tests.- 2.4 Testing a polyhedral-cone-shaped null hypothesis.- 3 A modification of the main problem: testing against a circular cone.- 3.0 Introduction and summary.- 3.1* An angular inequality constraint and the geometry of circular cones.- 3.2 Likelihood ratio tests for the modified problem.- 3.3* Computation of critical values of the likelihood ratio test statistics for the modified problem.- 3.4 A reduction of the modified problem by sufficiency and invariance.- 3.5 Easy-to-use combination procedures for the reduced modified problem.- 3.6* Other procedures for the reduced modified problem (?2=1).- 3.7 Some theory about the power properties of invariant tests (?2=1).- 3.8 Testing a circular-cone-shaped null hypothesis.- 4 Circular likelihood ratio tests for the main problem.- 4.0 Introduction and summary.- 4.1 Replacing the polyhedral cone K by some circular cone.- 4.2* Computation of the power of circular likelihood ratio (CLR-) tests (?2=1).- 4.3 Minimization of the maximum shortcoming of CLR-tests over K (?2=1).- 4.4 The minimax ray andangle of K for some particular cases.- 4.5 The maximin ray and angle of K for some particular cases.- 4.6 The use of CLR-tests.- 4.7 Power comparisons.- 4.8 Graphs of the minimax angle and the maximin angle of K for some particular cases.- 5 Applications.- 5.1 One-sided treatment comparison in the two-period crossover trial with binary outcomes.- 5.2 Test expectancy in educational psychology.- 5.3 Predatory behavior of hungry beetles.- 5.4 The assumption of double monotony in Mokken's latent trait model.- References and Author Index.- Appendices.