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In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance. This article primarily deals with efficiency of estimators. The relative efficiency of two procedures is the ratio of their efficiencies, although often this term is used where the comparison is made between a given procedure and a notional "best possible" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure. Efficiencies are often defined using the variance or mean square error as the measure of desirability. ==Estimators== The efficiency of an unbiased estimator, ''T'', of a parameter ''θ'' is defined as : where is the Fisher information of the sample. Thus ''e''(''T'') is the minimum possible variance for an unbiased estimator divided by its actual variance. The Cramér–Rao bound can be used to prove that ''e''(''T'') ≤ 1. 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「Efficiency (statistics)」の詳細全文を読む スポンサード リンク
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