NON ASYMPTOTIC EFFICIENCY OF A MAXIMUM LIKELIHOOD ESTIMATOR AT FINITE NUMBER OF SAMPLES (FriPmOR1)

Author(s) : Alexandre Renaux (SATIE UMR 8029, FRANCE) Philippe Forster (GEA IUT de Ville d'Avray, FRANCE) Eric Boyer (SATIE UMR 8029, FRANCE)

Abstract : In estimation theory, the asymptotic (with respect to the number of samples) efficiency of the Maximum Likelihood estimator is a well known result. Nevertheless, in some scenarios, the number of snapshots may be small. We recently investigated the asymptotic behavior of the Stochastic ML estimator at high Signal to Noise Ratio and finite number of samples in the array processing framework: we proved the non-Gaussiannity of the SML estimator and we obtained the analytical expression of the variance for the single source case. In this paper, we generalize these results to multiple sources, and we obtain variance expressions which demonstrate the non-efficiency of SML estimates.

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