# Bias and variance calculation for Ridge estimator of β

I understand how bias and variance for ridge estimator of β are calculated when the model is Y=Xβ + ϵ. But I have the model Y=Xtβ + ϵ. I don't understand if a model like that makes sense, can someone help me with that? If it does, how to derive the bias and variance for ridge estimator of β?

Thanks!

• I cannot imagine that the difference between the two models amounts to more than just notation. – Christoph Hanck Jun 2 at 11:52
• I don't know if that makes sense since in the usual Y=Xβ + ϵ model, Y is n x 1 matrix, X is n x k matrix, β is k x 1 matrix. If X is transposed, then X^t is k x n, on the other hand β is k x 1. How can they even multiply, then give Y as a result, which is n x 1. – user287169 Jun 2 at 12:25
• That is in principle correct, but without seeing the specific reference you deal with, that will be hard to answer. It might just be the case that, unusually, $X$ is defined as $k\times n$ in the second case. – Christoph Hanck Jun 2 at 12:38
• Yeah, that actually can be the case. Thanks! – user287169 Jun 4 at 18:35