## 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

Zbl 0918.62024
Full Text:

### References:

 [1] Anderson T.W., An Introduction to Multivariate Statistical Analysis,, 2. ed. (1984) · Zbl 0651.62041 [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) [5] Gleser, L. J. and Olkin, I. Estimation for a Regression Model with an Unknown Covariance Matrix. Proc. Sixth Berkeley Symp. Math. Statist. Prob. Edited by: Le Cam, L. M., Neyman, J. and Scott, E. Vol. 1, pp.pp. 541–568. Berkeley and Los Angeles, California: University of California Press. · Zbl 0232.62033 [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. [8] Siotani M., Modern Multivariate Statistical Analysis: A Graduate Course and Handbook (1985) · Zbl 0588.62068 [9] Srivastava M. S., An Introduction to Multivariate Statistics (1979) · Zbl 0421.62034 [10] DOI: 10.1016/0047-259X(89)90061-4 · Zbl 0686.62037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.