PMC Theorems on PCR–Ridge Class Estimators

After presenting the basic linear model and some definitions, the PMC superiority for a class of biased estimators is discussed. One objective of this paper is to develop such a methodology for the case when the squared statistical distance between the estimator and the parameter is used as the loss function, and that the estimators to be compared are linear combinations of common statistics having a multivariate normal distribution. To demonstrate the usefulness of the methodology, it is applied for the comparison of r-k$$r-k$$ class estimators with unbiased least squares estimator of regression coefficients.