2012.61: Covariance Structure Regularization via Entropy Loss Function
2012.61: Lijing Lin, Nicholas J. Higham and Jianxin Pan (2014) Covariance Structure Regularization via Entropy Loss Function. Computational Statistics & Data Analysis, 72. pp. 315-327. ISSN 0167-9473
This is the latest version of this eprint.
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. A new method is proposed for regularizing the covariance structure of a given covariance matrix whose underlying structure has been blurred by random noise, 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 comprising tridiagonal Toeplitz, compound symmetry, AR(1), and banded Toeplitz is considered. It is shown that for the first three structures local or global minimizers of the discrepancy can be computed by one-dimensional optimization, while for the fourth structure Newton's method enables efficient computation of the global minimizer. Simulation studies are conducted, showing that the proposed new approach provides a reliable way to regularize covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.
|Uncontrolled Keywords:||Covariance estimation; Covariance structure; Entropy loss function; Kullback-Leibler divergence; Regularization.|
|Subjects:||MSC 2000 > 62 Statistics|
MSC 2000 > 65 Numerical analysis
|Deposited By:||Dr Lijing Lin|
|Deposited On:||07 February 2014|
Available Versions of this Item
- Covariance Structure Regularization via Entropy Loss Function (deposited 07 February 2014) [Currently Displayed]