Alternative Estimation Procedures to OLS

Alternative Estimation Procedures to OLS We have seen that OLS does a nice job in model estimation when the CLRM assumptions are met. We have also seen that violations of the CLRM lead to inefficiency and estimators that are not BLUE. We have also seen that the model y=Xβ+ε can be transformed to produce estimators that are BLUE. We now consider additional estimation techniques to least squares. In truth, we’ve been using alternative estimators for some time. Recall generalized least squares. It is an alternative estimation procedure that places less weight on large errors and greater weight on small errors. Recall also that the sample size is important in the estimation process. Merging these two concepts together, we begin thinking about maximum likelihood estimators (MLE). MLEs are estimates of the parameters α, β and σ that maximize the likelihood of generating the random variables x1, . . . . . ,xn. Consider the normal distribution.