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jeza
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Mean Squared Error (MSE) of Ridge Regression

I am currently trying to understand the MSE of ridge regression.

First, I am calculating the MSE mathematically, but I found it quite vague.

After, reviewing some books and articles I understood that

$$MSE(\hat{\beta_R})=E[||\hat{\beta}_R-{\beta}||^2]$$ $$\Rightarrow\hat{\beta_{R}}-\beta=((X^TX+\lambda)^{-1}X^TX-I)\beta+e$$ $$\Rightarrow||\hat{\beta}_R-{\beta}||^2=(\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta})$$

After that I stuck because of the norm and expectation , I tried to solve it, but it becomes so complicated.

I checked books like: the elements of statistical learning and an introduction to statistical learning.

Can anyone please clarify MSE of ridge regression or guide me to a good source?

Many thanks.

jeza
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