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[1]

E ⁡ ‖ f n − f ‖ 2 2 = E ⁡ ∫ ( f n ( x ) − f ( x ) ) 2 d x {\displaystyle \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 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.

See also

  • Minimum distance estimation
  • Mean squared error

References

  1. ^ Wand, M. P.; Jones, M. C. (1994). Kernel smoothing. CRC press. p. 15.