  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.
