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Minimum distance estimation : ウィキペディア英語版
Minimum distance estimation
Minimum distance estimation (MDE) is a statistical method for fitting a mathematical model to data, usually the empirical distribution.
==Definition==
Let \displaystyle X_1,\ldots,X_n be an independent and identically distributed (iid) random sample from a population with distribution F(x;\theta)\colon \theta\in\Theta and \Theta\subseteq\mathbb^k (k\geq 1).
Let \displaystyle F_n(x) be the empirical distribution function based on the sample.
Let \hat be an estimator for \displaystyle \theta. Then F(x;\hat) is an estimator for \displaystyle F(x;\theta).
Let d() be a functional returning some measure of "distance" between the two arguments. The functional \displaystyle d is also called the criterion function.
If there exists a \hat\in\Theta such that d()=\inf\, then \hat is called the minimum distance estimate of \displaystyle \theta.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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