Existence conditions of the uniformly minimum risk unbiased estimators in extended growth curve models. (English) Zbl 0924.62057

Summary: Necessary and sufficient existence conditions are derived for the uniformly minimum risk unbiased estimators of the parameters in extended growth curve models with the general covariance matrix or the uniform covariance structure or the serial covariance structure under convex losses and matrix losses, respectively.


62H12 Estimation in multivariate analysis
62C20 Minimax procedures in statistical decision theory
62F10 Point estimation
Full Text: DOI


[1] Banken, L., Eine verallgemeinerung des GMANOVA modells, () · Zbl 0586.62079
[2] Geisser, S., Sample reuse procedures for prediction of the unobserved portion of a partially observed vector, Biometrika, 68, 243-250, (1981) · Zbl 0478.62054
[3] Lee, J.C.; Geisser, S., Application of growth curve prediction, Sankhya ser A, 37, 239-256, (1975) · Zbl 0352.62059
[4] Lehmann, E.L., Theory of point estimation, (1983), Wiley New York · Zbl 0522.62020
[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] Verbyla, A.P.; Venables, W.N., An extension of the growth curve model, Biometrika, 75, 129-138, (1988) · Zbl 0636.62073
[7] Von Rosen, D., Maximum likelihood estimates in multivariate linear normal models with special references to the growth curve model, ()
[8] Von Rosen, D., Maximum likelihood estimators in multivariate linear normal model, J. multivariate anal., 31, 187-200, (1989) · Zbl 0686.62037
[9] Von Rosen, D., Uniqueness conditions for maximum likelihood estimators in a multivariate linear model, J. statist. plann. inference, 36, 269-276, (1993) · Zbl 0778.62050
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.