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The random matrix regime of Maronna's M-estimator for observations corrupted by elliptical noises
This article studies the behavior of the Maronna robust scatter estimator
of a sequence of observations
which is composed of a dimensional signal drown in a heavy
tailed noise, i.e where and
is drawn from elliptical distribution.
In particular, we prove that as the population dimension , the number of
observations and the rank of grow to infinity at the same pace and
under some mild assumptions, the robust scatter matrix can be characterized by
a random matrix that follows a standard random model. Our analysis
can be very useful for many applications of the fields of statistical inference
and signal processing