Restricted expected multivariate least squares. (English) Zbl 1085.62068
Summary: A new approach of estimating parameters in multivariate models is introduced. A fitting function will be used. The idea is to estimate parameters so that the fitting function equals or will be close to its expected value. The function will be decomposed into two parts. From one part, which will be independent of the mean parameters, the dispersion matrix is estimated. This estimator is inserted in the second part which then yields the estimators of the mean parameters. The growth curve model, extended growth curve model and a multivariate variance components model will illustrate the approach.
MSC:
| 62H12 | Estimation in multivariate analysis |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 62J99 | Linear inference, regression |
Keywords:
Estimators; Growth curve model; Extended growth curve model; Least squares; Variance components; REMLSReferences:
| [1] | L. Banken, Eine Verallgemeinerung des GMANOVA Modells, Dissertation, University of Trier, Trier, Germany, 1984.; L. Banken, Eine Verallgemeinerung des GMANOVA Modells, Dissertation, University of Trier, Trier, Germany, 1984. · Zbl 0586.62079 |
| [2] | Khatri, C. G.; Shah, K. R., On the unbiased estimation of fixed effects in a mixed model for growth curves, Comm. Statist. A. Theory Methods, 10, 401-406 (1981) · Zbl 0449.62053 |
| [3] | Liang, K.-Y.; Zeger, S. L., Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22 (1986) · Zbl 0595.62110 |
| [4] | McCullagh, P.; Nelder, J. A., Generalized Linear Models (1989), Chapman & Hall: Chapman & Hall London · Zbl 0744.62098 |
| [5] | Potthoff, R. F.; Roy, S. N., A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51, 313-326 (1964) · Zbl 0138.14306 |
| [6] | von Rosen, D., Maximum likelihood estimators in multivariate linear normal models, J. Multivariate Anal., 31, 187-200 (1989) · Zbl 0686.62037 |
| [7] | von Rosen, D., The growth curve model: a review, Comm. Statist. Theory Methods, 20, 2791-2822 (1991) · Zbl 0800.62450 |
| [8] | von Rosen, D., Residuals in the Growth Curve model, Ann. Inst. Statist., 47, 129-136 (1995) · Zbl 0822.62046 |
| [9] | M.S. Srivastava, D. von Rosen, Growth curve models. Multivariate analysis, design of experiments, and survey sampling, Statistical Textbooks and Monogrgaph, vol. 159, Dekker, New York, 1999, pp. 547-578.; M.S. Srivastava, D. von Rosen, Growth curve models. Multivariate analysis, design of experiments, and survey sampling, Statistical Textbooks and Monogrgaph, vol. 159, Dekker, New York, 1999, pp. 547-578. · Zbl 1068.62513 |
| [10] | Verbyla, A. P.; Venables, W. N., An extension of the growth curve model, Biometrika, 75, 129-138 (1988) · Zbl 0636.62073 |
| [11] | Woolson, R. F.; Leeper, J. D., Growth curve analysis of complete and incomplete longitudinal data, Comm. Statist. A. Theory Methods, 9, 1491-1513 (1980) · Zbl 0449.62048 |
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