Admissible Estimator of the Eigenvalues of Variance-Covariance Matrix for Multivariate Normal Distributions--Detailed Proof--

TL;DR

This paper introduces an admissible estimator for the eigenvalues of the covariance matrix in multivariate normal distributions, providing a detailed proof of its properties under scale-invariant squared error loss.

Contribution

It presents a new admissible estimator for covariance eigenvalues with a rigorous proof of its optimality under specific loss functions.

Findings

Estimator is proven admissible under scale-invariant squared error loss.

Provides detailed mathematical proof of the estimator's properties.

Enhances understanding of covariance matrix eigenvalue estimation in multivariate analysis.

Abstract

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.