Advanced Econometrics is both a comprehensive text for graduate students and a reference work for econometricians. It will also be valuable to those doing statistical analysis in the other social sciences. Its main features are a thorough treatment of cross-section models, including qualitative response models, censored and truncated regression models, and Markov and duration models, as well as a rigorous presentation of large sample theory, classical least-squares and generalized least-squares theory, and nonlinear simultaneous equation models.

Although the treatment is mathematically rigorous, the author has employed the theorem-proof method with simple, intuitively accessible assumptions. This enables readers to understand the basic structure of each theorem and to generalize it for themselves depending on their needs and abilities. Many simple applications of theorems are given either in the form of examples in the text or as exercises at the end of each chapter in order to demonstrate their essential points.

This outstanding text by a foremost econometrician combines instruction in probability and statistics with econometrics in a rigorous but relatively nontechnical manner. Unlike many statistics texts, it discusses regression analysis in depth. And unlike many econometrics texts, it offers a thorough treatment of statistics. Although its only mathematical requirement is multivariate calculus, it challenges the student to think deeply about basic concepts.

The coverage of probability and statistics includes best prediction and best linear prediction, the joint distribution of a continuous and discrete random variable, large sample theory, and the properties of the maximum likelihood estimator. Exercises at the end of each chapter reinforce the many illustrative examples and diagrams. Believing that students should acquire the habit of questioning conventional statistical techniques, Takeshi Amemiya discusses the problem of choosing estimators and compares various criteria for ranking them. He also evaluates classical hypothesis testing critically, giving the realistic case of testing a composite null against a composite alternative. He frequently adopts a Bayesian approach because it provides a useful pedagogical framework for discussing many fundamental issues in statistical inference.

Turning to regression, Amemiya presents the classical bivariate model in the conventional summation notation. He follows with a brief introduction to matrix analysis and multiple regression in matrix notation. Finally, he describes various generalizations of the classical regression model and certain other statistical models extensively used in econometrics and other applications in social science.