= Exact mean integrated squared error of a kernel density estimator
{title2=$\operatorname{MISE}=R(K_h*f-f)+n^{-1}[R(K_h)-R(K_h*f)]$}
For independent observations with common density f, the <kernel density estimator> has mean $K_h*f$. Its pointwise variance is $n^{-1}[(K_h^2*f)-(K_h*f)^2]$. Integrate the variance and add integrated squared bias to get the displayed exact <mean integrated squared error>, assuming the integrals are finite. Since $R(K_h)=R(K)/h$, this also separates the smoothing bias from the stochastic variance.
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