Mean squared prediction error: Difference between revisions

Revision as of 09:45, 16 May 2018

Revision as of 21:59, 20 May 2018

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:<math>\operatorname{MSPE}(L)=\operatorname{E}\left[\left( g(x_i)-\widehat{g}(x_i)\right)^2\right].</math>

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 anotherthe other is the sum of variances of the fitted values:

:<math>\operatorname{MSPE}(L)=\sum_{i=1}^n\left(\operatorname{E}\left[\widehat{g}(x_i)\right]-g(x_i)\right)^2+\sum_{i=1}^n\operatorname{var}\left[\widehat{g}(x_i)\right].</math>