Robust Nonlinear Regression

4Heteroscedastic Variance

Nonlinear regression as defined in previous chapters assumed that errors are identically independent distributed (i.i.d.) with constant (homogeneous) variance. This chapter discuss the cases when the variance of the error is not homogeneous. The error variance is called heteroscedastic when it follows a functional relation with the predictor. In general it is a nonlinear function with some unknown parameters. Estimating heteroscedastic variance function parameters and fitting a nonlinear regression model with heteroscedastic variance is the subject of this chapter.

Heteroscedasticity of error variance is seen in real‐life examples for several reasons. A classic example (without outliers) is the chicken weight data presented by Riazoshams and Miri (2005) (Table A.1). The authors showed that the variance structure of the data is a power function of the nonlinear regression model . Although the variance can be a general function form of the predictor variable , in many applications it is observed the variance can be written as a function of the nonlinear regression model (an example will appear later on, in Figure 4.1).

As can be seen from the chicken weight data, ...