Synopses & Reviews
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. The analysis concludes with an examination of methods by which the possibility of misspecification can be empirically investigated and offers a variety of tests for misspecification.
Review
"...this often elegant and rigorous treatment of a wide variety of theoretical issues related to likelihood methods represents a useful contribution to the theoretical econometric literature on estimation and inference in possible misspecified models. The book should prove to be a useful reference book for econometric theorists. It should also be a useful reference and text for advanced graduate students wanting to learn about likelihood methods as well as the process of rigourous analysis of econometric methods in general." Journal of Economic Literature
Synopsis
This book examines the consequences of misspecifications from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference.
Table of Contents
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.