×

Consistent nonnegative estimates of variance components. (English) Zbl 1185.62049

Summary: The estimation of variance components in a linear mixed model with two random effects is investigated. The class of combination estimates based on the quadratic invariant statistics and consistent non-negative estimates are obtained. Furthermore, it is shown that the consistent non-negative estimate dominates the ANOVA estimate under some conditions.

MSC:

62F10 Point estimation
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
62H12 Estimation in multivariate analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baltgi, B.H. Econometric Analysis of Panel Data. John Wiley, New York, 1995
[2] Chen, X.R., Wang, S.G. The Least Square Method in Linear Model. Shanghai Science and Technology Press, Shanghai, 2003 (in Chinese)
[3] Efron, B., Morris, C. Families of minimax estimators of the mean of a multivariate normal distribution. Ann. Statist., 4(1): 11–21 (1976) · Zbl 0322.62010 · doi:10.1214/aos/1176343344
[4] Gnot, S., Kleffe, J., Zmylony, R. Nonnegativity of admissible invariant quadratic estimates in mixed linear models with two variance components. J. Statist. Plann. Inference, 12: 249–258 (1985) · Zbl 0572.62057 · doi:10.1016/0378-3758(85)90073-4
[5] Kelly, R.J., Mathew, T. Improved nonnegative estimation of variance components in some mixed models with unbalanced data. Technometrics, 36: 171–181 (1994) · Zbl 0925.62096 · doi:10.2307/1270229
[6] Kubokawa, T. A unified approach to improving equivariant estimators. Ann. Statist., 22(1): 290–299 (1994) · Zbl 0816.62021 · doi:10.1214/aos/1176325369
[7] LaMotte, L.R. On nonnegative quadratic unbiased estimation of variance components. J. Amer. Statist. Assoc., 68: 728–730 (1973) · Zbl 0271.62093 · doi:10.2307/2284808
[8] Mathew, T., Sinha, B.K. Nonnegative estimation of variance components in unbalanced mixed model with two variance components. J. Multivariate Anal., 42: 77–101 (1992) · Zbl 0777.62072 · doi:10.1016/0047-259X(92)90080-Y
[9] Rao, C.R., Kleffe, J. Estimation of Variance Components and Applications. North-Holland, New York, 1988 · Zbl 0645.62073
[10] Verbeke, G., Molenberghs, G. Linear Mixed Model for Longitudinal Data. Springer-Verlag, New York, 2000 · Zbl 0956.62055
[11] Wang, S.G., Chow, S.C. Advanced Linear Model. Marcel Dekker Inc., New York, 1994
[12] Wang, S.G., Shi, J.H., Yin, S.J., Wu, M.X. An Introduction to Linear Model. Academic Press, Beijing, 2004 (in Chinese)
[13] Wang, S.G., Yang, Z.H. Generalized Inverse Matrix and its Applications. Beijing University of Technology Press, Beijing, 1996 (in Chinese)
[14] Wang, S.G., Yin, S.J. A new estimate of the parameters in linear mixed models. Science in China, Ser. A, 45: 1301–1311 (2002) · Zbl 1098.62535
[15] Wu, M.X., Wang, S.G. Simultaneous optimal estimates of fixed effects and variance components in the mixed models. Science in China, Ser. A, 47: 787–799 (2004) · Zbl 1073.62060 · doi:10.1007/BF03036995
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.