LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS.

ABSTRACT: We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework allows us to exploit conditional sparsity covariance structure for the heavy-tailed data. In particular, for the elliptical distribution, we propose a robust estimator based on the marginal and

SUBMITTER: Fan J 

PROVIDER: S-EPMC6133289 | biostudies-literature | 2018 Aug

REPOSITORIES: biostudies-literature