2011/10/17 by Lipeng Ning, Ning, Lipeng, Xianhua Jiang +3 · 1 citation
Mathematics · Physics and Astronomy · #93E10 #93E12 #Advanced Differential Geometry Research #FOS: Electrical engineering #FOS: Mathematics #Morphological variations and asymmetry #Optimization and Control (math.OC) #Point processes and geometric inequalities #Statistics Theory (math.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1110.3695
openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and compare several alternatives metrics and divergence measures. We advocate a specific one which represents the Wasserstein distance between the corresponding Gaussians distributions and show that it coincides with the so-called Bures/Hellinger distance between covariance matrices as well. Most importantly, besides the physically appealing interpretation, computation of the metric requires solving a linear matrix inequality (LMI). As a consequence, computations scale nicely for problems involving large covariance matrices, and linear prior constraints on the covariance structure are easy to handle. We compare this transportation/Bures/Hellinger metric with the maximum likelihood and the Burg methods as to their performance with regard to estimation of power spectra with spectral lines on a representative case study from the literature.