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Unbiased invariant minimum norm estimation in generalized growth curve model

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  • Wu, Xiaoyong
  • Zou, Guohua
  • Chen, Jianwei

Abstract

This paper considers the generalized growth curve model subject to R(Xm)[subset, double equals]R(Xm-1)[subset, double equals]...[subset, double equals]R(X1), where Bi are the matrices of unknown regression coefficients, Xi,Zi and U are known covariate matrices, i=1,2,...,m, and splits into a number of independently and identically distributed subvectors with mean zero and unknown covariance matrix [Sigma]. An unbiased invariant minimum norm quadratic estimator (MINQE(U,I)) of tr(C[Sigma]) is derived and the conditions for its optimality under the minimum variance criterion are investigated. The necessary and sufficient conditions for MINQE(U,I) of tr(C[Sigma]) to be a uniformly minimum variance invariant quadratic unbiased estimator (UMVIQUE) are obtained. An unbiased invariant minimum norm quadratic plus linear estimator (MINQLE(U,I)) of is also given. To compare with the existing maximum likelihood estimator (MLE) of tr(C[Sigma]), we conduct some simulation studies which show that our proposed estimator performs very well.

Suggested Citation

  • Wu, Xiaoyong & Zou, Guohua & Chen, Jianwei, 2006. "Unbiased invariant minimum norm estimation in generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1718-1741, September.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1718-1741
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    References listed on IDEAS

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    1. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    2. DRYGAS, Hilmar, 1972. "The estimation of residual variance in regression analysis," LIDAM Reprints CORE 128, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Kleffe, J., 1979. "On Hsu's theorem in multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 442-451, September.
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    Cited by:

    1. Wu, Xiaoyong & Zou, Guohua & Li, Yingfu, 2009. "Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1061-1072, May.

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