Covariance estimation via fiducial inference.

Area of Science:

• Statistics
• Statistical Inference
• Covariance Estimation

Background:

• Covariance estimation is a classical statistical problem with extensive research in frequentist and Bayesian frameworks.
• Existing methods often require prior selection, which can introduce subjectivity and limit uncertainty quantification.

Purpose of the Study:

• To develop a novel fiducial approach for covariance matrix estimation.
• To quantify estimator uncertainty without requiring a prior distribution.
• To explore the application of this approach in identifying clique structures within covariance matrices.

Main Methods:

• The study leverages the Fiducial Bernstein-von Mises Theorem.
• A fiducial distribution for the covariance matrix is derived.
• Samples from the fiducial distribution are used for estimation and confidence region construction.

Main Results:

• The fiducial approach yields consistent estimators for the true covariance matrix.
• Meaningful confidence regions for the covariance matrix can be defined.
• The method demonstrates efficacy in identifying clique structures.

Conclusions:

• The developed fiducial approach offers a robust alternative for covariance estimation.
• It effectively quantifies uncertainty and provides reliable confidence intervals.
• This framework is a powerful tool for structural analysis of covariance matrices, including clique detection.