## Best Linear Unbiased Estimator

Neither of the two strategies discussed in Section 7.2.4 is the primary strategy of classical statisticians, although the second is less objectionable to them. Their primary strategy is that of defining a certain class of estimators within which we can find the best estimator in the sense of Definition 7.2.1. For example, in Example 7.2.1, if we eliminate W and Z from our consideration, T is the best estimator within the class consisting of only T and S. A certain degree of arbitrariness is unavoidable in this strategy. One of the classes most commonly considered is that of linear unbiased estimators. We first define

DEFINITION 7.2.4 0 is said to be an unbiasedestimator of 0 if £0 = 0 for

all 0 Є 0. We call £0-0 bias.

Among the three estimators in Example 7.2...

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