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Cleaning large-dimensional covariance matrices for correlated samples.

Zdzislaw Burda1, Andrzej Jarosz2

  • 1AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland.

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Summary

This study introduces a new method for estimating large covariance matrices, even with correlated samples. An efficient algorithm and open-source Python library are provided for practical applications.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Estimating large-dimensional covariance matrices is crucial in many fields.
  • Correlations between samples complicate traditional estimation methods.

Purpose of the Study:

  • To develop a robust method for estimating large covariance matrices with sample correlations.
  • To generalize existing estimators and provide practical tools.

Main Methods:

  • Utilizing random matrix theory and free probability.
  • Generalizing the Marčenko-Pastur equation and Ledoit-Péché shrinkage estimator.
  • Developing an efficient algorithm based on Ledoit-Wolf kernel estimation.

Main Results:

  • An efficient algorithm for analytic formulas is developed.
  • An open-source Python library named 'shrinkage' is released.
  • Demonstrated usage with synthetic data exhibiting autocorrelations.

Conclusions:

  • The developed method and library offer a user-friendly solution for large covariance matrix estimation.
  • The approach effectively handles sample correlations in high-dimensional data.