ABSTRACT
The linear models and covariance structures covered are wide-ranging and applicable in many different contexts. However, it is fair to ask how critical is the third ingredient that is the assumption of normal distributions, and whether this is really needed. The approach described in this chapter, Gaussian estimation, is to perform the same computations as before, obtaining parameter estimates from a normal likelihood, but then to see what modifications are necessary to make the inferences valid when normality might not obtain. The chapter presents straightforward linear regression examples, using small but manageable data sets. The purpose is to illustrate the construction and fitting of typical models for the mean vector and covariance matrix, not to present deep scientific investigations. A wide range of techniques is available nowadays. These include a variety of ways of looking at residuals, diagnostics, influence, tests for specific aspects of the model, and so on.
