I'm currently working through (part of) a textbook on nonparametric regression techniques. Regarding the choice of smoothing parameter the book starts out explaining the MSE which is defined as:

$MSE(\hat f(x)) = E[(\hat f(x)-f(x))^{2}]$

Would this really be the MSE? The book also mentiones the mean squared error of prediction (separately) but doesn't give a definition other than to explain that MSEP is for new values $(x^{*},y^{*})$.

I'm a bit confused as I've seen the term MSEP applied to the definition of MSE given by the book.

Thanks!

I'm currently working through (part of) a textbook on non-parametric regression techniques. Regarding the choice of smoothing parameter the book starts out explaining the MSE which is defined as:

$MSE(\hat f(x)) = E[(\hat f(x)-f(x))^{2}]$

Would this really be the MSE? The book also mentions the mean squared error of prediction (separately) but doesn't give a definition other than to explain that MSEP is for new values $(x^{*},y^{*})$.

I'm a bit confused as I've seen the term MSEP applied to the definition of MSE given by the book.

Thanks!