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Model averaging estimation for high-dimensional covariance matrices with a network structure.

Rong Zhu1, Xinyu Zhang2, Yanyuan Ma3

  • 1School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.

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|March 22, 2021
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Summary
This summary is machine-generated.

This study introduces a novel model averaging technique for estimating high-dimensional covariance matrices using polynomial functions. The method optimizes model weights for improved accuracy, demonstrated through simulations and a real-world airport network analysis.

Keywords:
Mallows criterionasymptotic optimalityconsistencycovariance regression network modelmodel averaging

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Area of Science:

  • Statistics
  • Econometrics
  • Network Analysis

Background:

  • High-dimensional covariance matrix estimation is crucial in various fields.
  • Existing methods face challenges with complex data structures.
  • Polynomial function-based models offer potential for improved estimation.

Purpose of the Study:

  • To develop a robust model averaging method for high-dimensional covariance matrix estimation.
  • To introduce a Mallows-type model averaging criterion for weight selection.
  • To validate the proposed method's performance and applicability.

Main Methods:

  • Constructing candidate models using polynomial functions of varying orders.
  • Proposing a Mallows-type model averaging criterion for weight selection.
  • Minimizing the criterion to obtain optimal weights, ensuring unbiased estimation.

Main Results:

  • The proposed model averaging method provides accurate high-dimensional covariance matrix estimates.
  • Asymptotic optimality of the model average covariance estimators is theoretically proven.
  • Numerical simulations and a case study confirm the method's practical utility.

Conclusions:

  • The developed model averaging approach offers a valuable tool for covariance matrix estimation.
  • The method demonstrates effectiveness in handling complex, high-dimensional data.
  • Applications include network structure analysis, as shown in the Chinese airport network case study.