Mean integrated squared error


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.

See also