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

Abstract

This paper addresses robust estimation of structured shape (normalized covariance) matrices. Shape matrices most often own a particular structure depending on the application of interest and taking this structure into account improves estimation accuracy. In the framework of robust estimation, we introduce a recursive robust shape matrix estimation technique based on Tyler’sM -estimate for convexly structured shape matrices. We prove that the proposed estimator is consistent, asymptotically efficient and Gaussian distributed and we notice that it reaches its asymptotic regime faster as the number of recursions increases. Finally, in the particular wide spreaded case of Hermitian persymmetric structure, we study the convergence of the recursions of the proposed algorithm.