statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, the mean integrated squared error (MISE) is used in density estimation. The MISE of an

estimate Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...

of an unknown probability density is given by :

\operatorname\, f_n-f\, _2^2=\operatorname\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 Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...

random variables. Here, E denotes the

expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...

with respect to that sample. The MISE is also known as ''L''²

risk function In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost ...

References

{{DEFAULTSORT:Mean Integrated Squared Error Estimation of densities Nonparametric statistics Point estimation performance

See also

References