Chapter 44
TESTING NON-NESTED HYPOTHESES
C. GOURIEROUX
CREST-CEPREMAP
A. MONFORT
CREST-INSEE
Contents
1. Introduction
2. Non-nested hypotheses
2.1. Definitions
2.2. Pseudo-true values
2.3. Semi-parametric hypotheses
2.4. Examples
2.5. Symmetry of the problem
3. Testing procedures
3.1. Maximum likelihood estimator under misspecification
3.2. The extended Wald test
3.3. The extended score test
3.4. The Cox procedure
3.5. Application to the choice of regressors in linear models
3.6. Applications to qualitative models
4. Artificial nesting models
4.1. Examples
4.2. Local expansions of artificial nesting models
4.3. A score test based on a modified Atkinson’s compound model
4.4. The partially modified Atkinson’s compound model
5. Comparison of testing procedures
5.1. Asymptotic equivalence of test statistics
5.2. Asymptotic comparisons of power functions
5.3. Exact finite sample results
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