• Source: 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




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

Kata Kunci Pencarian:

• Mean integrated squared error
• Loss function
• Mise
• List of statistics articles
• Kernel density estimation
• Mixture distribution
• Multivariate kernel density estimation
• Density estimation
• Histogram
• Bayes estimator