"MISE" redirects here. For other uses, see Mise.

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]

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

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References

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

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Kernel density estimation

parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ⁡ ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle

Loss function

{f}})=\|f-{\hat {f}}\|_{2}^{2}\,,} the risk function becomes the mean integrated squared error R ( f , f ^ ) = E ⁡ ( ‖ f − f ^ ‖ 2 ) . {\displaystyle R(f,{\hat

Mise

spectrometer aboard Europa Clipper MISE, an abbreviation for Mean integrated squared error All pages with titles containing Mise Mise en abyme Mise en

Local regression

estimates the mean-squared prediction error. Mallow's Cp and Akaike's Information Criterion, which estimate mean squared estimation error. Other methods

Mixture distribution

(2006, Ch.1.2.4) Marron, J. S.; Wand, M. P. (1992). "Exact Mean Integrated Squared Error". The Annals of Statistics. 20 (2): 712–736. doi:10.1214/aos/1176348653

Density estimation

accuracy. Frequency distribution Kernel density estimation Mean integrated squared error Histogram Multivariate kernel density estimation Spectral density

Normal distribution

}}^{2}} is better than the s 2 {\textstyle s^{2}} in terms of the mean squared error (MSE) criterion. In finite samples both s 2 {\textstyle s^{2}} and

Nonparametric statistics

squared error (MSE). L ( f , g ) = ‖ f − g ‖ L 2 ( X ) 2 {\displaystyle L(f,g)=\lVert f-g\rVert _{L^{2}({\mathcal {X}})}^{2}} : The Mean Integrated Square