Continuous mapping theorem: Difference between revisions

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In [[statistics]], the '''mean integrated squared error (MISE)''' is used in [[density estimation]]. The MISE of an [[estimator|estimate]] of an unknown [[probability density function|probability density]] is given by
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:<math>\operatorname{E}\|f_n-f\|_2^2=\operatorname{E}\int (f_n(x)-f(x))^2 \, dx</math>
 
where ''ƒ'' is the unknown density, ''ƒ''<sub>''n''</sub> is its estimate based on a [[sample (statistics)|sample]] of ''n'' [[independent and identically distributed]] random variables.  
Here, E denotes the [[expected value]] with respect to that sample.
 
The MISE is also known as ''L''<sup>2</sup> [[risk function]].
 
==See also==
* [[Minimum distance estimation]]
* [[Mean squared error]]
 
 
{{unreferenced|date=November 2010}}
 
{{DEFAULTSORT:Mean Integrated Squared Error}}
[[Category:Estimation of densities]]
[[Category:Non-parametric statistics]]
[[Category:Point estimation performance]]
 
 
{{statistics-stub}}

Latest revision as of 03:45, 14 September 2014

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