## Abstract

In the previous chapter procedures for augmenting the available sample information were considered. Consequences of incorporating nonsample information were seen to depend on the quality of information introduced. As one would expect, only the use of good information provides positive benefits. Unfortunately, we seldom are sure of the quality of the information to be introduced. In this chapter we examine the consequences of that uncertainty. First of all, investigators are in the habit of checking their prior nonsample information against the data using statistical tests of the type outlined in Chapter 6. The nonsample information is then either adopted or not depending upon the outcome of the test. The resulting estimation rule is called a preliminary test estimator since its form depends upon the outcome of a (preliminary) hypothesis test. This estimator is superior to the estimator based on sample information alone only over a relatively small portion of the parameter space, which reflects the fact that classical statistical procedures are not designed to aid the choice of a model specification. These results are discussed in Section 7.2.

## Keywords

Maximum Likelihood Estimator Risk Function Principal Component Regression Error Loss Noncentrality Parameter## Preview

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