Mean integrated squared error

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{{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{{cite book |last1=Wand |first1=M. P. |last2=Jones |first2=M. C. |title=Kernel smoothing |date=1994 |publisher=CRC press |pages=15}}

:$\backslash operatorname\{E\}\backslash |f\_n-f\backslash |\_2^2=\backslash operatorname\{E\}\backslash int\; (f\_n(x)-f(x))^2\; \backslash ,\; dx$

where ƒ is the unknown density, ƒ_n 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 L² risk function.