Covariance Structure Regularization via Entropy Loss Function

Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2012) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]

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Abstract

The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. We propose a new method for regularizing the covariance structure of a given covariance matrix, in which the underlying structure is usually blurred due to random noises particularly when the dimension of the covariance matrix is high. The regularization is made by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures such as tridiagonal, compound symmetry, AR(1), and Toeplitz are considered. Simulation studies are conducted, showing that the proposed new approach is reliable in regularization of covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.

Item Type: MIMS Preprint
Uncontrolled Keywords: Covariance estimation; Covariance structure; Entropy loss function; Kullback-Leibler divergence; Regularization
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User: Dr Lijing Lin
Date Deposited: 10 Sep 2013
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2020

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