Covariance matrix regularization for banded toeplitz structure via frobenius-norm discrepancy

Xiangzhao Cui , Zhenyang Li, Jine Zhao , Defei Zhang , Jianxin Pan

    Research output: Chapter in Book/Conference proceedingChapterpeer-review

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    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 Σ. 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 Σ. Our simulation studies show that B is also more accurate than the sample covariance matrix A when estimating the covariance matrix Σ that has a banded Toeplitz structure. The studies also show that the proposed method works very well in regularization of covariance structure.
    Original languageEnglish
    Title of host publicationMatrices, statistics andbBig data
    Subtitle of host publicationselected contributions from IWMS 2016
    EditorsS. Ejaz Ahmed, Francisco Carvalho, Simo Puntanen
    Place of PublicationSpringer, Cham
    PublisherSpringer Nature
    Pages111-125
    Number of pages15
    ISBN (Electronic)9783030175191
    ISBN (Print)9783030175184
    DOIs
    Publication statusPublished - 2019
    EventThe 25th International Workshop on Matrices and Statistics - Madeira, Portugal
    Duration: 6 Jun 20169 Jun 2016

    Conference

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

    Keywords

    • Covariance matrix structure
    • Frobenius norm
    • Regularization
    • Toeplitz structure

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