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

Alexandre Renaux (1) , Philippe Forster (2) , Eric Boyer (2)

1 L2S - Laboratoire des signaux et systèmes
2 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

In estimation theory, the asymptotic (in the number of samples) efficiency of the Maximum Likelihood (ML) estimator is a well known result [1]. Nevertheless, in some scenarios, the number of snapshots may be small. We recently investigated the asymptotic behavior of the Stochastic ML (SML) estimator at high Signal to Noise Ratio (SNR) and finite number of samples [2] 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.

Domains: Signal and Image Processing; Signal and Image processing

Alexandre Renaux, Philippe Forster, Eric Boyer. NON ASYMPTOTIC EFFICIENCY OF A MAXIMUM LIKELIHOOD ESTIMATOR AT FINITE NUMBER OF SAMPLES. European Signal Processing Conference, EUSIPCO-04, 2004, Vienne, Austria. ⟨inria-00444827⟩