Robust Nonlinear Regression

9Robust Nonlinear Regression in R

The nlr package discussed in Chapter 8 was produced to deal with the methods discussed in this book. There are another packages in the R language comprehensive archive for robust nonlinear regression. For example, the nlrq function in the nlrq package developed by Koenker and Park (1996) for quantile regression, the nlrob function in the robustbase package for M‐estimates using iterated reweighted least squares. These tools are explained in current chapter and will be compared with nlr, as presented in Chapter 8.

For comparison of the packages, a simulation study will be shown, because the exact values are known and the biases can therefore be computed. Then one easy and one complicated example will be illustrated.

The nlrq function from the nlrq package fits a nonlinear regression model by quantile regression. It was proposed by Koenker and Park (1996). It is a generalization of the least absolute ( norm) estimate shown in Equation (3.3).

The nlrob function in the robustbase package fits a nonlinear regression by iteratively reweighted least squares.

9.1 Lakes Data Examples

Consider the lakes data in Example 8.11. The MM‐estimate fitted by the nlr function is shown in the example. The quantile regression, least median squares (LMS), and ordinary least squares (OLS) estimates are shown at in the code below. The parameter estimates for the four methods ...