Abstract
This chapter presents five kinds of estimators: (1) least square estimators, (2) the generalized ridge regression estimator, (3) the mixed estimators, (4) the minimax estimator, and (5) the linear Bayes estimator. To obtain each kind of estimator, a different optimization problem is solved. Thus, each estimator is optimum with respect to a certain criterion of goodness. The chapter describes the concept of estimability, which is seen to be the criterion for uniqueness of least square estimators for the non-full rank model. It presents a proof of the Gauss–Markov Theorem. This theorem states that the least square estimator is the unbiased linear estimator with the smallest variance. The chapter presents a derivation of generalized ridge regression estimator.
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