Estimation, inference, and specification analysis

the long version

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 inference. 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. He then investigates the limiting distribution of the MLE under misspecification, the conditions under which MLE efficiency is not affected 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. . 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.