紹介
This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.
目次
1. Introductory remarks
2. Probability densities, likelihood functions and the quasi-maximum likelihood estimator
3. Consistency of the QMLE
4. Correctly specified models of density
5. Correctly specified models of conditional expectation
6. The asymptotic distribution of the QMLE and the information matrix equality
7. Asymptotic efficiency
8. Hypothesis testing and asymptotic covariance matrix estimation
9. Specification testing via m-tests
10. Applications of m-testing
11. Information matrix testing
12. Conclusion
Appendix 1. Elementary concepts of measure theory and the Radon-Nikodym theorem
Appendix 2. Uniform laws of large numbers
Appendix 3. Central limit theorems.
