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Book review

Author(s) Pázman, Andrej
Title Nonlinear Statistical Models
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Vasile Postolica

The research and the preparation of this book has been done during the author's work at the Mathematical Institute of the Slovak Academy of Sciences. It is a significant textbook concerning with nonlinear statistical models since it brings new results in this field and it presents the known results in an original manner.

Because the nonlinear regression model can be considered as an extension of the usual linear regression model, Chapter 1 is devoted to linear regression models. These considerations are very useful in Chapter 2 in order to establish linear properties of nonlinear models in the methods of statistical inference. The simpler one-parameter models are discussed in Chapter 3. Chapter 4 deals with the inner structure of the nonlinear models which in general is much more complicated than the linear models. Here we also find a connection with differential manifolds. The computation of estimators and curvatures in nonlinear regression models is treated in Chapter 5. Chapter 6 contains local approximations of probability densities and moments of estimators. The Chapters 7 and 8 are devoted to the global approximations of the probability density of estimators. Chapter 9 opens the topic of nonlinear exponential families considered as a generalization of the nonlinear regression models.

Beside the author's contributions concerning with the development of the usual finite sample geometric techniques, in this book there are many examples of nonlinear regression models in physics, chemical kinetics, agriculture, and econometrics. In accordance with the author's recommendation, this book is very useful for students in statistical modelling and an indispensable starting source for the scientists in this field or for anybody performing data processing by nonlinear regression. The book also includes bibliographical references, basic symbols, and a subject index.