# How to prove biased estimator with SVD of X [duplicate] Hi guys, I'm assuming that I am able to use SVD of X to solve this question. So, X = UΣV where U and V are nxn and pxp orthogonal matrices respectively and Σ is an nxp matrix containing the singular values on the diagonal.

I tried to get the expectation of both sides to show the biases. So RHS of the equation would be (1/λ)E[X'X]+E[β̂]=(1/λ)E[VΣ'ΣV']+E[β̂]. However, I am unable to prove (1/λ)E[VΣ'ΣV'] is not 0. Is this the right way to tackle this question? Any help would be appreciated!

## marked as duplicate by whuber♦Apr 2 '17 at 21:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• @whuber thanks for the link! I've got another question though. How do I prove the equation in the image? Why would there be a change in estimator when r=p? – meet Apr 2 '17 at 21:45
• I don't know, because you haven't explained what $r$ refers to. – whuber Apr 2 '17 at 21:50