Sparse and Low-Rank Covariance Matrices Estimation

Estimation of population covariance matrices from samples of multivariate data has draw many attentions in the last decade owing to its fundamental importance in multivariate analysis. With dramatic advances in technology in recent years, various research fields, such as genetic data, brain imaging, spectroscopic imaging, climate data and so on, have been used to deal with massive highdimensional data sets, whose sample sizes can be very small relative to dimension. In such settings, the standard and the most usual sample covariance matrices often performs poorly [1, 2, 11]. Fortunately, regularization as a class of new methods to estimate covariance matrices has recently emerged to overcome those shortages of using traditional sample covariance matrices. These methods encompass several specified forms, banding [1, 6, 17], tapering [4, 10] and thresholding [2, 5, 8, 16] for instance.