Statistical Tools for Nonlinear Regression

1. Front Matter

   Pages i-ix

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2. Nonlinear regression model and parameter estimation

   • Sylvie Huet, Annie Bouvier, Marie-Anne Gruet, Emmanuel Jolivet

   Pages 1-27

3. Accuracy of estimators, confidence intervals and tests

   • Sylvie Huet, Annie Bouvier, Marie-Anne Gruet, Emmanuel Jolivet

   Pages 29-59

4. Variance estimation

   • Sylvie Huet, Annie Bouvier, Marie-Anne Gruet, Emmanuel Jolivet

   Pages 61-88

5. Diagnostics of model misspecification

   • Sylvie Huet, Annie Bouvier, Marie-Anne Gruet, Emmanuel Jolivet

   Pages 89-130

6. Calibration and Prediction

   • Sylvie Huet, Annie Bouvier, Marie-Anne Gruet, Emmanuel Jolivet

   Pages 131-147

7. Back Matter

   Pages 149-155

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If you need to analyze a data set using a parametric nonlinear regression model, if you are not on familiar terms with statistics and software, and if you make do with S-PLUS, this book is for you. In each chapter we start by presenting practical examples. We then describe the problems posed by these examples in terms of statistical problems, and we demonstrate how to solve these problems. Finally, we apply the proposed methods to the example data sets. You will not find any mathematical proofs here. Rather, we try when possible to explain the solutions using intuitive arguments. This is really a cook book. Most of the methods proposed in the book are derived from classical nonlinear regression theory, but we have also made attempts to provide you with more modern methods that have proved to perform well in practice. Although the theoretical grounds are not developed here, we give, when appropriate, some technical background using a sans serif type style. You can skip these passages if you are not interested in this information. The first chapter introduces several examples, from experiments in agron­ omy and biochemistry, to which we will return throughout the book. Each example illustrates a different problem, and we show how to methodically handle these problems by using parametric nonlinear regression models.

• Biology
• STATISTICA
• Statistics
• data analysis
• linear regression

From the reviews of the second edition:

"Users of S-PLUS or R who do nonlinear estimation would certainly want a copy of this book. The wealth of applications and code for using the specialized software transcends the limitation of the applications to medicine and biology." Technometrics, May 2004

"In this second edition to the first edition published in 1996, the authors present a comprehensive overview of nonlinear regression methods. With an emphasis on learning the basics of how to perform analyses using S-PLUS or R and understand and present the results, the book provides a valuable resource for those interested in learning this material...The book is easy to read, and the inclusion of S-PLUS output, graphs, and source code makes picking up the book and getting started much easier. For those working with data best modeled by nonlinear relationships, this book will be a valuable addition to your shelf of resources." Journal of the American Statistical Association, September 2004

"As the title suggests, the book deals with non-linear regression analysis … . The real strength of the book lies in a careful and detailed discussion of a number of examples … . Anyone who is interested in actually analysing data using non-linear models will benefit from working through these examples … . the book would make an excellent secondary source for a course in non-linear models. … A number of excellent references are available that provide the necessary theoretical background … ." (Christopher Cox, Statistics in Medicine, Vol. 24 (13), 2005)

"This second edition provides a comprehensive overview of the field of parametric nonlinear regression models in data analysis. The book aims especially at students, as a tutorial book, and at the scientists applying statistical methods in different practical domains. Each chapter begins with a set of different concrete examples, followed by the corresponding statistical issues and solutions. Inaddition, where necessary, a very simple theoretical background is provided." (Florin Gorunescu, Zentralblatt MATH, Vol. 1041 (16), 2004)

"The first 5 chapters of this book discuss normal distribution models where the mean is described with a nonlinear model. Chapter six discusses a nonlinear model with a binomial distribution, chapter seven uses a Poisson and multinomial distribution. … The large amount of examples … makes this book a valuable contribution to the every day statistical practice." (J. van den Broek, Kwantitatieve Methoden, Issue 72B34, 2004)

"This book describes itself as a ‘cookbook’ for non-linear regression and is supported by the nls2 software … . The chapters are reasonably and logically laid out … . There are 42 references, many of which are to other text-books on modeling … . The back cover suggests that it may be of use to students as a tutorial book. It is certainly a valuable complement to the nls2 software … ." (Paul Hewson, Journal of the Royal Statistical Society, Vol. 198 (1), 2005)

• INRA Laboratoire de Biométrie, Jouy-en-Josas Cedex, France

  Sylvie Huet, Annie Bouvier, Marie-Anne Gruet

• INRA SESAMES, Paris Cedex 07, France

  Emmanuel Jolivet

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