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What is the exact definition of precision of a statistical estimator? Any references to textbooks are appreciated.

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Precision is typically defined as the reciprocal of the variance of an estimator. A high variance estimator has low precision and vice versa.

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    $\begingroup$ Would it be better to say "the reciprocal" instead of "1 over" to account for precision matrices? $\endgroup$
    – Neil G
    Apr 25, 2012 at 23:56
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Precision can be defined as 1/variance, or 1/standard deviation. See Wikipedia's article on Normal distribution (section "Alternative formulations") and references provided therein.

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