Robust Nonlinear Regression

2Nonlinear Models: Concepts and Parameter Estimation

2.1 Introduction

This chapter presents the basic concepts, notation, and theories of nonlinear regression that are used in this book. Nonlinear regression can be represented as a more general functional form of linear regression. Some models in nonlinear regression can therefore be approximated by linear expansions. There are, however, differences that should be taken into consideration. Although linear regression and linear models can be used to describe several statistical models, it is unreasonable to assume that linear models are sufficient. However, the theoretical and computational difficulties of nonlinear regression have resulted in its being neglected and sometimes forgotten by statisticians.

Powerful computational tools and efficient numerical algorithms have been developed for nonlinear modelling. In particular, several R packages for nonlinear regression have been developed, and these are discussed in this book. In general, estimation methods in nonlinear regression require the application of numerical algorithms, which are also explored in this book. Finally, numerical methods for robust nonlinear regression are explained, and an R package called nlr, which was developed by the author, is discussed.

In applied sciences, there are appropriate methods for constructing nonlinear models for a statistics data set in certain phenomena. For example, differential equation models are widely used in biostatistics and agriculture ...