A matrix inequality and its statistical application Original Research Article

Let A1,…,As be nonnegative definite matrices. We prove that there are constants ci, 1less-than-or-equals, slantiless-than-or-equals, slants, depending on A1,…,As such that for all positive numbers x1,…,xs,imagewhere I represents the identity matrix. The result is applied to statistical inference about mixed linear models to show the existence of moments of complex estimators including the maximum likelihood and restricted maximum likelihood estimators of the variance components, and the empirical best linear unbiased estimators (predictors) of the fixed (random) effects.