Point Estimation Methods

Abstract

In our discussion of point estimation, we have yet to present any generally applicable procedures that lead to specific functional forms for estimators of q(Θ) and that can be relied upon to define estimators that generally have good estimator properties. In fact, the only result in the previous chapter that could be used directly to define the functional form of an estimator is the theorem on the attainment of the CRLB, which is useful only if the statistical model {f(x; Θ), Θ ∈ Ω{ and the estimand q(Θ) are such that the CRLB is actually attainable. Of course, we did examine a number of important results that could be used either to narrow the search for a good estimator of q(Θ), to improve upon an unbiased estimator that we already discovered, or to recognize when an unbiased estimator was actually the best in the sense of minimizing variance (or in the sense of having the smallest covariance matrix). However, since the functional form of an estimator of q(Θ) having good estimator properties is often not apparent even with the aid of the results assembled in Chapter 7, we now examine procedures that suggest functional forms of estimators.