Abstract
In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix.We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1 orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. F. Pothoff and S. N. Roy, “A Generalized Multivariate Analysis of Variance Model Useful Especially for Growth Curve Problems”, Biometrika 51, 313–326 (1964).
A. P. Verbyla and W. N. Venables, “An Extension of the Growth Curve Model”, Biometrika 75 (1), 129–138 (1988).
D. von Rosen, “Maximum Likelihood Estimators in Multivariate Linear Normal Models”, J. Multivar. Anal. 31 (2), 187–200 (1989).
T. Kollo and D. von Rosen, Advanced Multivariate Statistics with Matrices (Springer, Dordrecht, 2005).
K. Filipiak and D. von Rosen, “On MLEs in an Extended Multivariate Linear Growth Curve Model”, Metrika 75 (8), 1069–1092 (2012).
J. Hu, “Properties of the Explicit Estimators in the Extended Growth Curve Model”, Statistics 44 (5), 477–492 (2010).
J. Hu, G. Yan, and J. You, “Estimation for an Additive Growth Curve Model with Orthogonal Design Matrices”, Bernoulli 17 (4), 1400–1419 (2011).
J. C.-S. Lee and S. Geisser, “Applications of Growth Curve Prediction”, Sankhyā: The Indian J. Statist., Ser. A 37 (2), 239–256 (1975).
J. C. Lee, “Prediction and Estimation of Growth Curves with Special Covariance Structures”, J. Amer. Statist. Assoc. 83 (402), 432–440 (1988).
C. G. Khatri, “Testing Some Covariance Structures under a Growth Curve Model”, J. Multivar. Anal. 3 (1), 102–116 (1973).
M. Ohlson and D. von Rosen, “Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured Covariance Matrices”, J. Multivar. Anal. 101 (5), 1284–1295 (2010).
J. Nzabanita, M. Singull, and D. von Rosen, “Estimation of Parameters in the Extended Growth Curve Model with a Linearly Structured Covariance Matrix”, Acta et Commentationes Universitatis Tartuensis de Mathematica 16 (1), 13–32 (2012).
C. G. Khatri, “Some results for the singular normal multivariate regression models”, Sankhyā: The Indian J. Statist., Ser. A, 267–280 (1968).
H. Cramér, Mathematical Methods of Statistics (Princeton Univ. Press, Princeton, 1946).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Nzabanita, J., von Rosen, D. & Singull, M. Extended GMANOVA model with a linearly structured covariance matrix. Math. Meth. Stat. 24, 280–291 (2015). https://doi.org/10.3103/S1066530715040031
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066530715040031