Modified estimator of the contribution rates of population eigenvalues

TL;DR

This paper introduces modified estimators for population eigenvalue contribution rates under elliptical distributions, reducing bias and improving accuracy over classical estimators in principal component and factor analysis.

Contribution

It proposes new bias-reducing estimators for eigenvalue contribution rates and proves their theoretical superiority over classical estimators.

Findings

Modified estimators decrease bias of classical sample contribution rates.

Theoretical risk analysis shows improved performance of the new estimators.

Numerical checks confirm correction of underestimation issues in PCA and factor analysis.

Abstract

Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The improvement of the modified estimators over the classical estimator are proved theoretically in view of their risks. We also checked numerically that the drawback of the classical estimator, namely the underestimation of the dimension in principal component analysis or factor analysis, are corrected in the modification.