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.