Closed-form estimator for the matrix-variate Gamma distribution

In this paper we present a novel closed-form estimator for the parameters of the matrix-variate gamma distribution. The estimator relies on the moments of a transformation of the observed matrices, and is compared to the maximum likelihood estimator (MLE) through a simulation study. The study reveals that when the underlying scale matrix parameter is ill-conditioned, or when the shape parameter is close to its lower bound, the suggested estimator outperforms the MLE, in terms of sample estimation error. In addition, since the suggested estimator is closed-form, it does not require numerical optimization as the MLE does, thus needing shorter computation time and is furthermore not subject to start value sensitivity or convergence issues. Finally, regarding the case of general parameter values, using the proposed estimator as start value in the optimization procedure of the MLE is shown to substantially reduce computation time, in comparison to using arbitrary start values.