The Kullback-Leibler divergence was introduced in a paper titled “On Information and [this property].” For 10 points each:
[10h] Name this property of a statistic that allows it to be conditioned-on to produce estimators with equal or lesser variance by the Rao-Blackwell theorem. Writing exponential family PDFs in canonical form allows easy identification of statistics that have both completeness and this property.
ANSWER: sufficiency [or sufficient or sufficient statistic]
[10m] Complete and sufficient statistics can be used to construct these estimators, named for two desirable properties and usually abbreviated as a three or four letter acronym. If an efficient estimator exists, it is also one of these estimators.
ANSWER: MVUE [or MRUE; accept UMVUE or uniformly minimum-variance unbiased estimator; accept UMRUE or uniformly minimum-risk unbiased estimator]
[10e] Sufficient statistics were developed by this British eugenicist, who also developed ANOVA and names a type of statistical “information.”
ANSWER: Ronald Aylmer Fisher [or R.A. Fisher; accept Fisher information]
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