Nonlinear regression analysis and its applications.

*(English)*Zbl 0728.62062
Wiley Series in Probability and Mathematical Statistics. New York etc.: John Wiley & Sons. xiv, 365 p. (1988).

We have tried to give a balanced presentation of the theory and practice of nonlinear regression. We expect readers to have a working knowledge of linear regression. Nevertheless, to provide background material and to establish notation, we give a summary review of linear least squares in Chapter 1, together with a geometrical development which is helpful in understanding both linear and nonlinear least squares. On the practical side, we discuss linear least squares in the context of modern computing methods and present useful material for checking the assumptions which are involved in regression and for modifying and improving fitted models. In Chapter 2 we discuss how nonlinear models can arise, and show how linear regression methods can be used iteratively to estimate the parameters. We also show how linear methods can be used to make approximate inferences about parameters and nonlinear model functions: again, the geometry is emphasized. The practical aspects of nonlinear estimation are discussed fully in Chapter 3, including such topics as getting starting values, transforming parameters, derivative-free methods, dealing with correlated residuals and with accumulated data, and comparing models.

In Chapter 4 we cover special methods for dealing with multiresponse data, and in Chapter 5 special techniques for compartment models, in which the response function is specified as the solution to a set of linear differential equations.

In Chapter 6 we discuss improved methods for presenting the inferential results of a nonlinear analysis, using likelihood profile traces and profile t plots. Finally, in Chapter 7 we present material concerned with measuring how badly nonlinear a particular model-data set situation is. This chapter is helpful in understanding and appreciating the geometry of nonlinear least squares - and indeed, of linear least squares.

Extensive displays of geometrical constructs have been used to facilitate understanding. We have also used continuing examples so that readers can follow the development of ideas in manageable steps within familiar contexts. All of the data sets used in this book are real, that is, the data were obtained from genuine physical, chemical, and biological experiments.

In Chapter 4 we cover special methods for dealing with multiresponse data, and in Chapter 5 special techniques for compartment models, in which the response function is specified as the solution to a set of linear differential equations.

In Chapter 6 we discuss improved methods for presenting the inferential results of a nonlinear analysis, using likelihood profile traces and profile t plots. Finally, in Chapter 7 we present material concerned with measuring how badly nonlinear a particular model-data set situation is. This chapter is helpful in understanding and appreciating the geometry of nonlinear least squares - and indeed, of linear least squares.

Extensive displays of geometrical constructs have been used to facilitate understanding. We have also used continuing examples so that readers can follow the development of ideas in manageable steps within familiar contexts. All of the data sets used in this book are real, that is, the data were obtained from genuine physical, chemical, and biological experiments.

##### MSC:

62J02 | General nonlinear regression |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |