Covariance Matrix Regularization for Banded Toeplitz Structure via Frobenius-Norm Discrepancy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

  • Authors:
  • Xiangzhao Cui
  • Zhenyang Li
  • Jine Zhao
  • Defei Zhang
  • Jianxin Pan

Abstract

In many practical applications, the structure of covariance matrix is often
blurred due to random errors, making the estimation of covariance matrix very
difficult particularly for high-dimensional data. In this article, we propose a regularization method for finding a possible banded Toeplitz structure for a given covariance matrix A (e.g., sample covariance matrix), which is usually an estimator of the unknown population covariance matrix S. We aim to find a matrix, say B, which is of banded Toeplitz structure, such that the Frobenius-norm discrepancy between B and A achieves the smallest in the whole class of banded Toeplitz structure matrices. As a result, the obtained Toeplitz structured matrix B recoveries the underlying structure behind S. Our simulation studies show that B is also more accurate than the sample covariance matrix A when estimating the covariance matrix S that has a banded Toeplitz structure. The studies also show that the proposed method works very well in regularization of covariance structure.

Bibliographical metadata

Original languageEnglish
Title of host publicationIWMS 2016 Madeira Springer Proceedings: Matrices, Statistics and Big Data
StateAccepted/In press - 17 Feb 2017
EventThe 25th International Workshop on Matrices and Statistics - Madeira, Portugal

Conference

ConferenceThe 25th International Workshop on Matrices and Statistics
Abbreviated titleIWMS'2016
CountryPortugal
CityMadeira
Period6/06/169/06/16