ABSTRACT
This chapter presents the use of best linear unbiased estimates in order to estimate both the fixed parameters and the random errors in the mixed linear model. These estimates depend on the ratios of the variance components. Given these components, the estimates can be expressed as the solution to a regression problem. The chapter reviews C. R. Henderson’s estimates, estimates of the variance components based on likelihood methods, and a robust extension of these methods. In the variance-component model, each observation is formed from the sum of several random errors. Henderson’s method maximizes the diagnostic information for the residuals associated with the largest variance components. By contrast, the method of unweighted means maximizes the diagnostic information for the residuals highest in the nesting hierarchy. Thus parameter estimates reflect the body of the data, and the nonoutlying residuals are better able to display other departures from the assumed model.
