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A Cholesky-based estimation for large-dimensional covariance matrices.

Xiaoning Kang1, Chaoping Xie2, Mingqiu Wang3

  • 1International Business College and Institute of Supply Chain Analytics, Dongbei University of Finance and Economics, Dalian, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for estimating large-dimensional covariance matrices without variable ordering. The new technique combines multiple estimates, ensuring a positive definite and applicable solution for complex datasets.

Keywords:
Cholesky factorensemble estimatelarge-dimensionalordering of variablespositive definite

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Estimating large-dimensional covariance matrices is challenging, especially when variables lack a natural ordering.
  • Existing methods may struggle with high dimensionality and the absence of inherent variable sequences.

Purpose of the Study:

  • To develop a robust and applicable method for estimating large-dimensional covariance matrices.
  • To address the challenge of variable ordering in covariance matrix estimation.
  • To propose an estimator that is positive definite and suitable for high-dimensional data.

Main Methods:

  • Utilizing a modified Cholesky decomposition technique.
  • Generating multiple covariance matrix estimates under various variable orderings.
  • Constructing the final estimator as a linear combination of individual estimates and the identity matrix.

Main Results:

  • The proposed estimator is demonstrated to be positive definite.
  • The method is shown to be applicable in large-dimensional settings.
  • Numerical studies and a real data example confirm the estimator's effectiveness compared to existing methods.

Conclusions:

  • The new method provides a reliable approach for large-dimensional covariance matrix estimation.
  • The technique effectively handles situations where variables have no natural ordering.
  • The proposed estimator offers advantages in terms of positive definiteness and applicability.