A TWO-STAGE ESTIMATOR OF INDIVIDUAL REGRESSION COEFFICIENTS IN MULTIVARIATE LINEAR GROWTH CURVE MODELS.
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Beganu, G. (2023). A TWO-STAGE ESTIMATOR OF INDIVIDUAL REGRESSION COEFFICIENTS IN MULTIVARIATE LINEAR GROWTH CURVE MODELS. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 30(117), 549–550. https://doi.org/10.18257/raccefyn.30(117).2006.2282

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Abstract

Se considera una familia de modelos lineales de curvas de crecimiento multivariadas con efectos aleatorios. El propósito del artículo es describir un método de cálculo para la estimación de coeficientes de regresión individuales cuando las componentes de covarianza sean conocidas o no. En el segundo caso, la matriz de covarianza de los datos se estimará usando una versión generalizada del método III de Henderson mediante proyecciones ortogonales sobre subespacios lineales que corresponden al modelo y se obtiene un estimador en dos etapas para los coeficientes individuales de regresión. Se presenta la estimación de efectos fijos y aleatorios usando un abordaje bayesiano.

https://doi.org/10.18257/raccefyn.30(117).2006.2282

Keywords

Estimated empirical Bayes estimator | quadratic unbiased estimator | orthogonal projection
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References

Baksalary, J.K. and Kala, R. (1979), Criteria for estimability in multivariate linear models, Math. Operationsforsch. Statist. ser. Statist., 7, 5-9.

Beganu, G. (1987), Estimation of regression parameters in a covariance linear model, Stud. Cerc. Mat., 39, 3-10.

Beganu, G. (1987), Estimation of covariance components in linear models. A coordinate-free approach, Stud. Cerc. Mat., 39, 228-233.

Beganu, G. (2003), The existence conditions of the best linear unbiased estimators of the fixed factor effects, Econom. Cumput. Econom. Cybernet. Studies and Research, 36, 95-102.

Beganu, G. Quadratic estimator of covariance components in a multivariate mixed linear model, Statistical Methods and Applications (to appear).

Beganu, G. (2005), On Gram-Schmidt orthogonalizing process of design matrices in linear models as estimating procedure of covariance components, Rev. R. Acad. Cien. Serie A. Mat., 99, 187-194.

Chen, Z. and Dunson, D. B. (2003), Random effects selection in linear mixed models, Biometrics, 59, 762-771.

De Gruttola, V.; Ware, J. H. and Louis, T.A. (1987), Influence analysis of generalized least squares estimators, J. Amer. Statist. Assoc., 82, 911-917.

Dempster, A. P.; Laird, N. M. and Rubin, D. B. (1977), Maximum likelihood from incomplete data via the EM algorithm, J. Royal Statist. Soc., Ser. B, 39, 1-38.

Dempster A. P.; Rubin, D. B. and Tsutakawa, R. K. (1981), Estimation in covariance components models, J. Amer. Statist. Assoc., 76, 341-353.

Eaton, M. L. (1970). Gauss-Markov estimation for multivariate linear models: A coordinate free approach, Ann. Math. Statist., 41, 528-538.

Halmos, P. R. (1958), Finite Dimensional Vector Spaces, 2nd ed., Van Nostrand, Princeton, New Jersey.

Harville, D. A. (1976), Extension of the Gauss-Markov theorem to include the estimation of random effects, Ann. Statist, 4, 384-305.

Harville, D. A. (1977), Maximum likelihood approaches to variance component estimation and to related problems, J. Amer. Statist. Assoc., 72, 320-340.

Henderson, C. R. (1953), Estimation of variance and covariance components, Biometrics, 9, 226-252.

Khan, S. and Powell J.L. (2001), Two-step estimation of semiparametric censored regression models, J. Econometrics, 103, 73-110.

Khuri, A. I. (1992), Response surface models with random block effects, Technometrics, 34, 26-37.

Laird, N. M. and Ware, J. H. (1982), Random-effects models for longitudinal data, Biometrics, 38, 963-974.

Lange, N. and Laird, N. M. (1989). The effect of covariance structure on variance estimation in balanced growth-curve models with random parameters, J. Amer. Statist. Assoc., 84, 241-247.

Morris, C.N. (1983), Parametric empirical Bayes inference: Theory and applications, J. Amer. Statist. Assoc., 78, 47-55.

Neudecker, N. (1990), The variance matrix of a matrix quadratic form under normality assumptions. A derivation based on its moment-generating function, Math. Operationsforsch. Statist., ser. Statistics, 3, 455-459.

Potthoff, R. F. and Roy, S. N. (1964), A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51, 313-326.

Prassad, N. G. N. and Rao, J. N. K. (1990), The estimation of the mean squared error of small-area estimators, J. Amer. Statist. Assoc., 85, 163-171.

Reinsel, G. (1982), Multivariate repeated-measurement or growth curve models with multivariate random-effects covariance structure, J. Amer. Statist. Assoc., 77, 190-195.

Reinsel, G. (1984), Estimation and prediction in a multivariate random effects generalized linear model, J. Amer. Statist. Assoc., 79, 406-414.

Reinsel, G. (1985), Mean squared error properties of empirical Bayes estimators in a multivariate random effects general linear model, J. Amer. Statist. Assoc., 80, 642-650.

Sala-Martin, X., Doppelhofer, G. and Miller, R. I. (2004), Determinants of long-term growth: A Bayesian averaging of classical estimates (BACE) approach, American Economic Review, 94, 813-835.

Smouse E. P. (1984), A note on Bayesian least squares inference for finite population models, J. Amer. Statist. Assoc., 70, 390-392.

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