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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Consistent estimator ： ウィキペディア英語版 Consistent estimator In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter ''θ''0—having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to ''θ''0. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to ''θ''0 converges to one. In practice one constructs an estimator as a function of an available sample of size ''n'', and then imagines being able to keep collecting data and expanding the sample ''ad infinitum''. In this way one would obtain a sequence of estimates indexed by ''n'', and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value ''θ''0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency as defined here is sometimes referred to as ''weak consistency''. When we replace convergence in probability with almost sure convergence, then the estimator is said to be ''strongly consistent''. Consistency is related to bias; see bias versus consistency. == Definition == Loosely speaking, an estimator ''Tn'' of parameter ''θ'' is said to be consistent, if it converges in probability to the true value of the parameter: : $$ \underset is a family of distributions (the parametric model), and } is an infinite sample from the distribution ''pθ''. Let be a sequence of estimators for some parameter ''g''(''θ''). Usually ''Tn'' will be based on the first ''n'' observations of a sample. Then this sequence is said to be (weakly) consistent if : $$ \underset) = g(\theta),\ \ \text\ \theta\in\Theta. This definition uses ''g''(''θ'') instead of simply ''θ'', because often one is interested in estimating a certain function or a sub-vector of the underlying parameter. In the next example we estimate the location parameter of the model, but not the scale: 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「Consistent estimator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.