Mean Squared Prediction Error - Estimation of MSPE

Estimation of MSPE

For the model where, one may write

The first term is equivalent to

$\sum_{i=1}^n\left(\operatorname{E}\left-g(x_i)\right)^2 =\operatorname{E}\left-\sigma^2\operatorname{tr}\left.$

Thus,

If is known or well-estimated by, it becomes possible to estimate MSPE by

Colin Mallows advocated this method in the construction of his model selection statistic Cp, which is a normalized version of the estimated MSPE:

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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