A Note on Superiority Comparisons of Homogeneous Linear Estimators

This note extends some results on homogeneous linear estimators to the general, even nonlinear case.A Sufficient condition for the difference of mean square error matrices of minimum conditional mean square error estimator and minimum average risk linear estimator to be postive definite is derived.     

A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations

We discuss here an alternative approach for decreasing the bias of the closed-form estimators for the gamma distribution recently proposed by Ye and Chen in 2017. We show that, the new estimator has also closed-form expression, is positive, and can be computed for n?>?2. Moreover, the corrective approach returns better estimates when compared with the former ones.     

A note on the estimation of the integral of ⨍2(x)

The estimation of $\text{γ=∫}{}^{\mathrm{\infty }}{}_{\mathrm{?\infty }}\text{?}{}^2\text{(x)dx}$, important in nonparametric inference, is discussed. Methods, based on either density estimators or on the lengths of nonparametric confidence intervals, are compared. We conclude that density type estimators have advantages over the estimators based on confidence intervals.