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In statistics the mean squared prediction error of a smoothing procedure is the expected sum of squared deviations of the fitted values from the (unobservable) function . If the smoothing procedure has operator matrix , then
The MSPE can be decomposed into two terms just like mean squared error is decomposed into bias and variance; however for MSPE one term is the sum of squared biases of the fitted values and another the sum of variances of the fitted values:
Note that knowledge of is required in order to calculate MSPE exactly.
Estimation of MSPEEdit
For the model where , one may write
The first term is equivalent to
If is known or well-estimated by , it becomes possible to estimate MSPE by
where comes from that fact that the number of parameters estimated for a parametric smoother is given by , and is in honor of Cuthbert Daniel.
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