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 by¹

${\displaystyle \operatorname {E} \|f_{n}-f\|_{2}^{2}=\operatorname {E} \int (f_{n}(x)-f(x))^{2}\,dx}$

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.