Minimum Variance Linear Unbiased Estimation

Finally, consider the problem of finding a linear unbiased estimator. If we seek the one which has smallest variance, we will be led once again to least squares. This proposition will be proved in Section 4.4.

The preceding does not assert that no other competing estimator would ever be preferable to least squares. We have restricted attention to linear estimators. The result immediately above precludes what might be an acceptably biased estimator. And, of course, the assumptions of the model might themselves not be valid. Although A5 and A6 are ultimately of minor consequence, the failure of any of the first four assumptions would make least squares much less attractive than we have suggested here.

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