In this note, we provide an elementary analysis of the prediction error ridge regression with random design. The proof is short and self-contained. particular, it bypasses use Rudelson’s deviation inequality for covariance matrices, through a combination exchangeability arguments, matrix perturbation operator convexity.

Modified (r, k) class ridge regression (MCRR) which includes unbiased ridge regression (URR), (r, k) class, principal components regression (PCR) and the ordinary least squares (OLS) estimators is proposed in regression analysis, to overcome the problem of multicollinearity. In this paper, we derive the necessary and sufficient conditions for the superiority of the MCRR estimator over each of t...