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Extremum estimator : ウィキペディア英語版
Extremum estimator
In statistics and econometrics, extremum estimators is a wide class of estimators for parametric models that are calculated through maximization (or minimization) of a certain ''objective function'', which depends on the data. The general theory of extremum estimators was developed by .
== Definition ==
An estimator \scriptstyle\hat\theta is called an extremum estimator, if there is an ''objective function'' \scriptstyle\hat_n such that
:
\hat\theta = \underset_n(\theta),

where Θ is the possible range of parameter values. Sometimes a slightly weaker definition is given:
:
\widehat Q_n(\hat\theta) \geq \max_\,\widehat Q_n(\theta) - o_p(1),

where ''o''''p''(1) is the variable converging in probability to zero. With this modification \scriptstyle\hat\theta doesn’t have to be the exact maximizer of the objective function, just be sufficiently close to it.
The theory of extremum estimators does not specify what the objective function should be. There are various types of objective functions suitable for different models, and this framework allows us to analyse the theoretical properties of such estimators from a unified perspective. The theory only specifies the properties that the objective function has to possess, and when one selects a particular objective function, he or she only has to verify that those properties are satisfied.

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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