# Mean integrated squared error

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Mean integrated squared error

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

$\operatorname{E}\|f_n-f\|_2^2=\operatorname{E}\int (f_n(x)-f(x))^2 \, dx$

where ƒ is the unknown density, ƒn is its estimate based on a sample of n iid random variables. Here, E denotes the expected value with respect to that sample.

The MISE is also known as L2 risk function.