Existence conditions of the uniformly minimum risk unbiased estimators in extended growth curve models

Wu, Qi-Guang

doi:10.1016/s0378-3758(97)00119-5

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…Obviously, a further and challenging research is on obtaining results similar to those obtained in the article for the EGCM subject to the nested conditions rank(X 1 ) + p ≤ n and C (X 1 ) ⊇ C (X 2 ) ⊇ · · · ⊇ C (X k ) in Equation (2), the assumption used in [6,7,16].…”

Section: Discussionmentioning

confidence: 74%

“…For instance, von Rosen [6] derived the maximum likelihood estimators of parameter matrices in the EGCM with the following nested subspace conditions of the treatment design matrices rank(X 1 ) + p ≤ n and C (X 1 ) ⊇ C (X 2 ) ⊇ · · · ⊇ C (X k ), (2) where C (X) denotes the column space of X. With the nested subspace conditions, Wu [7] obtained the uniformly minimum risk unbiased estimators of the parameter matrices under convex losses and matrix losses, respectively. Žežula [8] also investigated two-components model in the EGCM.…”

Section: J Humentioning

confidence: 99%

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Properties of the explicit estimators in the extended growth curve model

2010

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be the extended growth curve model with error matrix E distributed as a normal distribution with mean 0 and covariance I ⊗ , subject to some specified conditions. A quadratic statistiĉ (Y ), distributed as a Wishart distribution, is proposed and proved to be a uniformly minimum variance unbiased invariant estimator of the second-order parameter matrix . In addition, unbiased and explicit estimatorsˆ i (Y) of the first-order parameter matrices i are given. And explicit formulae to compute the traces of the covariance matrices ofˆ i (Y) are derived.

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Section: Discussionmentioning

confidence: 74%

Section: J Humentioning

confidence: 99%

Properties of the explicit estimators in the extended growth curve model

2010

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“…It usually means that we have some information about correlation structure. Two most common such models are (a) uniform correlation model Wu [6,7] proposed a method for the estimation of 2 and in the uniform structure model which is rather complicated (and due to typo undecipherable) and is very difficult to generalize to more complicated models. Therefore, we would like to have a simpler estimator which is applicable also in other situations.…”

Section: Standard Modelmentioning

confidence: 99%

“…(see [6,Theorem 3.1]). It is easy to see that if r(X) = m < n and r(Z) = r < p, Tr(Y Y ), 1 Y Y 1, P Y Q can be replaced by Tr(Y Y ), 1 Y Y 1, ZY X .…”

Section: Uniform Correlation Structurementioning

confidence: 99%

Special variance structures in the growth curve model

Žežula

2006

Journal of Multivariate Analysis

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Standard and extended growth curve model (multivariate linear model) with practically important variance structures are considered and a method for parameters estimation is proposed. Standard modelLet us consider standard growth curve modelwhere Y n×p is a matrix of multivariate observations, X n×m is an ANOVA design matrix, Z r×p is a regression constants matrix, B m×r is a matrix of unknown (the first order) parameters and ε n×p is a matrix of random errors. Matrix of the unknown second order parameters describes the dependence of the columns of Y.There is no problem estimating when it is completely unknown. Problems, however, arise when its structure is partially known. It usually means that we have some information about * Fax: +421 55 6222124.

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“…Von Rosen (1993) also gave the necessary and sufficient existence conditions for the maximum likelihood estimators of unknown parameters. Wu (1998) derived the necessary and sufficient conditions for the uniformly minimum risk unbiased estimators of the parameters of the first order. He considered three different structures of unknown matrix :…”

Section: Introductionmentioning

confidence: 99%