Herman J. Bierens - Böcker

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

In this book Herman Bierens provides a mathematically rigorous treatment of a number of timely topics in advanced econometrics. His subjects include nonlinear estimation, maximum likelihood theory, ARMA and ARMAX models, unit roots and cointegration, and nonparametric regression, together with an extensive and thorough treatment of the necessary probability theory. Professor Bierens' study is uniquely self-contained, providing the reader with a selection of the latest developments in econometric theory, along with the required introductory material on each topic. It will be of great use to graduate students of econometrics and statistics, and is particularly suitable for self-tuition.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

The papers collected in the two volumes Nonlinear Models focus on the asymptotic theory of parameter estimators of nonlinear single equation models and systems of nonlinear models, in particular weak and strong consistency, asymptotic normality, and parameter inference, for cross-sections as well as for time series. A selection of papers on testing for, and estimation and inference under, model misspecification is also included. The models under review are parametric, hence their functional form is assured to be known up to a vector of unknown parameters, and the functional form involved is nonlinear in at least one of the parameters.The selection of earlier articles on nonlinear parametric models is extensive and, although they are not all equally influential, each has played a significant part in the development of the field. The more recent articles have been selected on the basis of their potential importance for the further development of this sphere of study.