{{more citations needed|date=February 2022}} {{Redirect|MISE|other uses|Mise (disambiguation){{!}}Mise}} In statistics, the '''mean integrated squared error (MISE)''' is used in density estimation. The MISE of an estimate of an unknown probability density is given by<ref>{{cite book |last1=Wand |first1=M. P. |last2=Jones |first2=M. C. |title=Kernel smoothing |date=1994 |publisher=CRC press |pages=15}}</ref>
:<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 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
==References== {{Reflist}}
{{DEFAULTSORT:Mean Integrated Squared Error}} Category:Estimation of densities Category:Nonparametric statistics Category:Point estimation performance