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In statistics, Fisher consistency, named after Ronald Fisher, is a desirable property of an estimator asserting that if the estimator were calculated using the entire population rather than a sample, the true value of the estimated parameter would be obtained. == Definition == Suppose we have a statistical sample ''X''1, ..., ''X''''n'' where each ''X''''i'' follows a cumulative distribution ''F''''θ'' which depends on an unknown parameter ''θ''. If an estimator of ''θ'' based on the sample can be represented as a functional of the empirical distribution function ''F̂n'': : the estimator is said to be ''Fisher consistent'' if: :〔Cox, D.R., Hinkley D.V. (1974) ''Theoretical Statistics'', Chapman and Hall, ISBN 0-412-12420-3. (defined on p287)〕 As long as the ''X''''i'' are exchangeable, an estimator ''T'' defined in terms of the ''X''''i'' can be converted into an estimator ''T′'' that can be defined in terms of ''F̂n'' by averaging ''T'' over all permutations of the data. The resulting estimator will have the same expected value as ''T'' and its variance will be no larger than that of ''T''. If the strong law of large numbers can be applied, the empirical distribution functions ''F̂n'' converge pointwise to ''Fθ'', allowing us to express Fisher consistency as a limit — the estimator is ''Fisher consistent'' if : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fisher consistency」の詳細全文を読む スポンサード リンク
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