Handbook of nonlinear regression models. (English) Zbl 0705.62060

Statistics: Textbooks and Monographs, 107. New York etc.: Marcel Dekker, Inc. ix, 241 p. (1990).
The handbook is divided into two parts. Part I consists of three chapters. Here the background to nonlinear regression modelling and the philosophy of it are discussed. In the first chapter an introduction to regression is given. Especially the connection of regression with functional and structural relationships is considered. In chapter 2, nonlinear models are discussed and here a proposal for the distance between linear and nonlinear models is given. Chapter 3 details, by means of an illustrative example, many aspects of regression.
Part II of the handbook deals with the nonlinear models themselves. The models are to be classified according to the shape of curve, within a category determined by the number of explanatory variables. The chapters 4 to 6 deal with models with only one explanatory variable. Thus in chapter 4 are to be considered convex (concave) curves. Then in the next chapter one discusses sigmoidally shaped curves. Chapter 6 is devoted to models with curves with maxima and minima.
Chapter 7 deals with models having more than one explanatory variable. In Chapter 8 one finds results on models which are not falling into the chapters 4 to 7. In chapter 9, the computational aspects are discussed. Thus, the choice of the initial parameter in approximation procedures is discussed. At the end one finds in chapter 10 a nice summary and concluding remarks.
The book contains a lot of interesting results for nonlinear regression. It is of interest for students and statisticians who are working in applied problems. It is a good handbook, it is clearly written and very well understandable.
Reviewer: H.Liero


62J02 General nonlinear regression
62-02 Research exposition (monographs, survey articles) pertaining to statistics