Mean integrated squared error

In density estimation, the mean integrated squared error (MISE) of an estimate of an unknown probability density is given by

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

where f is the unknown density, $f_{n}$ is its estimate based on a random sample of n iid random variables. E denotes the expected value with respect to that sample.

The MISE is also known as $L^{2}$ risk function.

See also

• Mean squared error