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.

Econometric Model Specification reviews and extends the author's papers on consistent model specification testing and semi-nonparametric modeling and inference. This book consists of two parts. The first part discusses consistent tests of functional form of regression and conditional distribution models, including a consistent test of the martingale difference hypothesis for time series regression errors. In the second part, semi-nonparametric modeling and inference for duration and auction models are considered, as well as a general theory of the consistency and asymptotic normality of semi-nonparametric sieve maximum likelihood estimators. Moreover, this volume also contains addendums and appendices that provide detailed proofs and extensions of all the results. It is uniquely self-contained and is a useful source for students and researchers interested in model specification issues.

This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate if the distributions of both the errors and the regressors have fat tails. This study also improves and extends the NL2SLSE theory of Amemiya. The method involved is a variant of the instrumental variables method, requiring at least as many instrumental variables as parameters to be estimated. The new MIE method requires less instrumental variables. Asymptotic normality can be derived by employing only one instrumental variable and consistency can even be proved with out using any instrumental variables at all."

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.

This book is intended for use in a rigorous introductory Ph.D. 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.