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

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.