Robust-COMET for covariance estimation in convex structures: Algorithm and statistical properties

On the Recursions of Robust COMET Algorithm for Convexly Structured Shape Matrix

“…The vector µ is the unknown parameter of interest, with exact value µ e and M e = M (µ e ). We recall that Tr [M e ] = m. The RCOMET estimate, µ 0 , of µ e is obtained by [13]…”

“…. , y N with (2) 2: Initialize µ 0 with (4) 3: for k = 1 to K do 4: Compute µ k from (6) 5: end for 6: return µ K M (µ e )) and asymptotically efficient and Gaussian distributed [13].…”

“…The standard semi-definite program solver, CVX, is used to compute this estimator [21]. The related CRB, CRB U , is also drawn for the comparison [13]. Fig.…”

“…the common Complex Angular Elliptical (CAE) distribution. Several robust methods have been proposed to leverage Tyler's estimator formulation [7] in the context of structured shape matrices [8]- [13]. A COnvexly ConstrAined (COCA) shape matrix estimator has been recently proposed in [10].…”

“…A COnvexly ConstrAined (COCA) shape matrix estimator has been recently proposed in [10]. Iterative Majorization-Minimization algorithms for the computation of structured CM estimates are developped in [11] and a robust extension of COMET, named RCOMET, has been derived in [13]. The references [8], [9], [12] considered the problem of robust shape matrix estimation with symmetric structures.…”