Linear approximate Bayes estimator for variance components in random effects model*

Abstract We employ a linear Bayes procedure to estimate the variance components in a random effects model and propose a linear approximate Bayes estimator (LABE) for the variance components, which has an analytical closed form and is easy to use. Numerical simulations show that the proposed LABE is very close to the ordinary Bayes estimator and even performs better than the Lindley’s approximation. Furthermore, we compare the LABE with the Tierney and Kadane’s approximation by simulations and also compare it with the restricted maximum likelihood estimator in the simulations and a real data case. The superiorities of the proposed LABE over the classical estimators are also investigated in terms of the mean squared error matrix (MSEM).

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