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Simultaneous confidence regions in an extended growth curve model with \(k\) hierarchical within-individuals design matrices. (English) Zbl 1009.62043

Summary: We consider an extended growth curve model with \(k\) hierarchical within-individuals design matrices. The model includes the one whose mean structure consists of polynomial growth curves with \(k\) different degrees. First we propose certain simple estimators of the mean and covariance parameters which are closely related to the MLE’s. Using these estimators we construct simultaneous confidence regions for each or all of \(k\) growth curves, which is an extension of Y. Fujikoshi [Commun. Stat., Theory Methods 28, No. 3-4, 671-682 (1999; Zbl 0918.62024)]. A numerical example with \(k=3\) is also given.

MSC:

62H12 Estimation in multivariate analysis
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 0918.62024
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References:

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[2] DOI: 10.1080/03610929908832319 · Zbl 0918.62024
[3] DOI: 10.1023/A:1004035330761 · Zbl 0977.62060
[4] Fujikoshi Y., J. Japan Statist. Soc. 13 pp 151– (1983)
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[6] DOI: 10.2307/2528795
[7] Rao, C. R. Least Squares Theory Using an Estimated Dispersion Matrix and Its Application to Measurement of Signals. Proc. Fifth Berkeley Symp. Math. Statist. Prob. Edited by: Le Cam, L. M. and Neyman, J. Vol. 1, pp.pp. 355–372. Berkeley and Los Angeles, California: University of California Press.
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[10] DOI: 10.1016/0047-259X(89)90061-4 · Zbl 0686.62037
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