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Modified estimators of the contribution rates of population eigenvalues

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  • Sheena, Yo

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 is 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.

Suggested Citation

  • Sheena, Yo, 2013. "Modified estimators of the contribution rates of population eigenvalues," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 301-316.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:301-316
    DOI: 10.1016/j.jmva.2012.10.014
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    References listed on IDEAS

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    1. Sadanori Konishi, 1977. "Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 389-396, December.
    2. John Mandel, 1972. "Principal components, analysis of variance and data structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 26(3), pages 119-129, September.
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    Cited by:

    1. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    2. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.

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