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Estimation of parameters in the growth curve model via an outer product least squares approach for covariance

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  • Hu, Jianhua
  • Liu, Fuxiang
  • Ahmed, S. Ejaz

Abstract

In this paper, we propose a framework of outer product least squares for covariance (COPLS) to directly estimate covariance in the growth curve model based on an analogy, between the outer product of a data vector and covariance of a random vector, and the ordinary least squares technique. The COPLS estimator of covariance has an explicit expression and is shown to have the following properties: (1) following a linear transformation of two independent Wishart distribution for a normal error matrix; (2) having asymptotic normality for a nonnormal error matrix; and (3) having unbiasedness and invariance under a linear transformation group. And, a corresponding two-stage generalized least squares (GLS) estimator for the regression coefficient matrix in the model is obtained and its asymptotic normality is investigated. Simulation studies confirm that the COPLS estimator and the two-stage GLS estimator of the regression coefficient matrix are satisfying competitors with some evident merits to the existing maximum likelihood estimator in finite samples.

Suggested Citation

  • Hu, Jianhua & Liu, Fuxiang & Ahmed, S. Ejaz, 2012. "Estimation of parameters in the growth curve model via an outer product least squares approach for covariance," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 53-66.
    • Handle: RePEc:eee:jmvana:v:108:y:2012:i:c:p:53-66
    DOI: 10.1016/j.jmva.2012.02.007
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    References listed on IDEAS

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    1. Hu, Jianhua, 2008. "Wishartness and independence of matrix quadratic forms in a normal random matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 555-571, March.
    2. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    3. Ohlson, Martin & von Rosen, Dietrich, 2010. "Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1284-1295, May.
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    1. Veronika Kopčová & Ivan Žežula, 2020. "On intraclass structure estimation in the growth curve model," Statistical Papers, Springer, vol. 61(3), pages 1085-1106, June.
    2. Hu, Jianhua & Xin, Xin & You, Jinhong, 2014. "Model determination and estimation for the growth curve model via group SCAD penalty," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 199-213.

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