by Qiang Gao, updated at Apr 23, 2017
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Under Assumptions 1.1–1.4, does there exist a linear, but not necessarily unbiased, estimator of $$ \boldsymbol{\beta} $$ that has a variance smaller than that of the OLS estimator? If so, how small can the variance be?
If an estimator of $$ \boldsymbol{\beta} $$ is a constant, then the estimator is trivially linear in $$ \mathbf{y} $$.
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