On the Maximum Likelihood Estimator Statistics for Unimodal Elliptical Distributions in the High Signal-to-Noise Ratio Regime

In this letter, we study the behavior of the maximum likelihood estimator (MLE) in the framework of low noise level (or high signal-to-noise ratio), when the data follow a unimodal elliptical distribution. The MLE appears to be the same as in the Gaussian context, regardless the noise distribution. We also show that the asymptotic distribution of this estimator is unimodal elliptical, where the law is intimately linked to that of the noise distribution. Additionally, this estimator is shown to be not efficient, except in the Gaussian noise case. Finally, we validate our analytic results by some simulations.