Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models

New matrix, determinant and trace versions of the Kantorovich inequality (KI) involving two positive definite matrices are presented. Some of these are used to study the efficiencies of minimum-distance (MD) estimators, generalized method-of-moments (GMM) estimators and several estimators specific to longitudinal or panel-data analysis. They are also used to give upper bounds for the determinant and trace of the asymptotic variance matrix of a weighted least-squares (WLS) estimator in the generalized linear model.