Testing Problems with Linear or Angular Inequality Constraints
Represents a self-contained account of a new promising and generally applicable approach to a large class of one-sided testing problems, where the alternative is restricted by at least two linear inequalities. It highlights the geometrical structure of these problems. It gives guidance in the constr...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1990, 1990
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| Edition: | 1st ed. 1990 |
| Series: | Lecture Notes in Statistics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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
- 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