Robust Nonlinear Regression

3Robust Estimators in Nonlinear Regression

Classical assumptions – independence, homogeneity of error variances, normality of errors, and many others – might not be satisfied in real‐life data. Some of these null conditions, such as heteroscedasticity of error variances and autocorrelated errors, will be discussed in later chapters.

The classical assumptions of a regression model may not be met in real‐life data. In particular, outliers may breach those classical assumptions; their effect will therefore be to mislead. To show these effects, Figure 3.1 displays some simulated data generated from the logistic model , in which the errors are generated from an independent normal distribution with constant variance. Several artificial outliers are then added to the data and parameters are estimated using the classical least squares estimator.

Figure 3.1 Simulated logistic model, artificially contaminated. (a) Logistic model: solid line, least squares estimate; dashed line, robust MM‐estimate. (b) Computed residuals. Upper chart: least squares estimate; lower chart: MM‐estimate.

The plot not only shows that the parameter estimates are wrong, but also mistakenly suggests the errors are dependent, ...