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On MLEs in an extended multivariate linear growth curve model

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  • Katarzyna Filipiak

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  • Dietrich Rosen
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    Abstract

    In this paper the extended growth curve model is considered. The literature comprises two versions of the model. These models can be connected by one-to-one reparameterizations but since estimators are non-linear it is not obvious how to transmit properties of estimators from one model to another. Since it is only for one of the models where detailed knowledge concerning estimators is available (Kollo and von Rosen, Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005 ) the object in this paper is therefore to present uniqueness properties and moment relations for the estimators of the second model. One aim of the paper is also to complete the results for the model presented in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005 ). The presented proofs of uniqueness for linear combinations of estimators are valid for both models and are simplifications of proofs given in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005 ). Copyright The Author(s) 2012

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    File URL: http://hdl.handle.net/10.1007/s00184-011-0368-2
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    Bibliographic Info

    Article provided by Springer in its journal Metrika.

    Volume (Year): 75 (2012)
    Issue (Month): 8 (November)
    Pages: 1069-1092

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    Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1069-1092

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    Related research

    Keywords: Extended growth curve model; Maximum likelihood estimators; Moments; Estimability;

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    1. Kunert, Joachim & Martin, R. J., 2000. "On the determination of optimal designs for an interference model," Technical Reports 2000,17, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Katarzyna Filipiak & Rafał Różański, 2009. "Connectedness of complete block designs under an interference model," Statistical Papers, Springer, vol. 50(4), pages 779-787, August.
    3. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
    4. Markiewicz, Augustyn, 2001. "On dependence structures preserving optimality," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 415-419, July.
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