Nonlinear Statistical Models by A. Ronald Gallant John Wiley & Sons, 1986

This book fills a gap in the statistical and econometric literature in providing a book-length discussion of nonlinear models and their statistical asymptotic theory. Despite its encompassing title, the book deals exclusively with nonlinear regression models and nonlinear simultaneous equation models (in a static and in a dynamic setting) from the general viewpoint as exposited in the review article by Burguete, Gallant, and Souza [6]. Models with censored data or models for qualitative data, for example, which legitimately may also be viewed as nonlinear statistical models, are not discussed in the book. Developments in nonlinear time series analysis in the last fifteen years as discussed in the books by Tong [14] and Subba Rao and Gabr [13] are other topics which are also not covered by the book. Basically, the book presents the work of the author and his co-workers in the field of nonlinear models over the last fifteen years. A general feature of the book is the considerable variation in the level of presentation. For example, on the one hand simple facts like Taylor's Theorem are explained in detail, while on the other hand much more advanced concepts like weak convergence of probability measures on the space D[G,1] are explained very shortly. This unevenness in the presentation is partly caused by the attempt to make the book accessible to a reader without sufficient background in analysis and probability theory. But it makes the book in points clumsy to read and I doubt that a reader unfamiliar with the more advanced concepts will get a good grasp of them by reading only the relevant portions of this book and not consulting the relevant literature for background information. To help the theoretically less proficient reader almost every result is illustrated by numerical examples. Although this may be helpful to such a reader, it is rather a nuisance if one wants to follow the main text. The main text is permanently interrupted by these examples, and as they extend over pages it is sometimes easy to miss the point where the main discussion continues. These examples consist not only of numerical calculations but also contain computer code and extensive tables. Of course, this consumes a lot of space. For example, Chapter 1 is made up of examples and