A Note on Comparison of (Non) Linear Estimators Using Pitman's Measure of Closeness

We present some sufficient and necessary conditions under which some linear (or nonlinear) estimators (see Sections 2 and 3) dominate (are better than) others in the sense of PMC. Its applications in linear regressions are also discussed. Furthermore, we obtain results about the eigenvalues of two matrices, which seem to be hard to be prove through pure matrix theory.