Properties of the explicit estimators in the extended growth curve model

Hu, Jianhua

doi:10.1080/02331880903236884

Cited by 8 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(3) Σ(Y ) is an unbiased invariant estimator of Σ; see [5]. A similar result for the growth curve model was obtained by Žežula [18].…”

supporting

confidence: 60%

Estimation for an additive growth curve model with orthogonal design matrices

Hu¹,

Yan²,

You

2011

Bernoulli

Self Cite

View full text Add to dashboard Cite

An additive growth curve model with orthogonal design matrices is proposed in which observations may have different profile forms. The proposed model allows us to fit data and then estimate parameters in a more parsimonious way than the traditional growth curve model. Two-stage generalized least-squares estimators for the regression coefficients are derived where a quadratic estimator for the covariance of observations is taken as the first-stage estimator. Consistency, asymptotic normality and asymptotic independence of these estimators are investigated. Simulation studies and a numerical example are given to illustrate the efficiency and parsimony of the proposed model for model specifications in the sense of minimizing Akaike's information criterion (AIC).

show abstract

“…(3) Σ(Y ) is an unbiased invariant estimator of Σ; see [5]. A similar result for the growth curve model was obtained by Žežula [18].…”

supporting

confidence: 60%

Estimation for an additive growth curve model with orthogonal design matrices

Hu¹,

Yan²,

You

2011

Bernoulli

Self Cite

View full text Add to dashboard Cite

show abstract

“…The conditions (2) and (3) lead to different parametrizations of the model (1), however, Filipiak and von Rosen [1] showed that via reparametrization one can derive model with condition (3) from model with condition (2) or vice versa, i.e. the two models are equivalent.…”

Section: Introductionmentioning

confidence: 97%

“…In Model II Filipiak and von Rosen [1] gave also the MLEs of unknown parameters for the three component model and they discussed the uniqueness conditions and the moments for MLEs. Hu [2] came up with a modification of Model I, assuming that the column spaces of betweenindividual design matrices are orthogonal, i.e.…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood estimators for extended growth curve model with orthogonal between-individual design matrices

Klein

Žežula

2015

Statistical Methodology

View full text Add to dashboard Cite

“…For example in Filipiak and von Rosen (2012), the explicit MLEs are presented with the nested subspace conditions on the within design matrices instead. In (Hu, 2010, Hu et al, 2011, the extended growth curve model without nested subspace conditions but with orthogonal design matrices is considered and generalized least-squares estimators and their properties are studied.…”

Section: Estimation In Bilinear Regression Modelsmentioning

confidence: 99%

Bilinear and Trilinear Regression Models with Structured Covariance Matrices

Nzabanita

2015

Linköping Studies in Science and Technology. Dissertations

View full text Add to dashboard Cite

Joseph Nzabanita (2015). Bilinear and Trilinear Regression Models with Structured Covariance Matrices Doctoral dissertation. This thesis focuses on the problem of estimating parameters in bilinear and trilinear regression models in which random errors are normally distributed. In these models the covariance matrix has a Kronecker product structure and some factor matrices may be linearly structured. Most of techniques in statistical modeling rely on the assumption that data were generated from the normal distribution. Whereas real data may not be exactly normal, the normal distributions serve as a useful approximation to the true distribution. The modeling of normally distributed data relies heavily on the estimation of the mean and the covariance matrix. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model's estimated mean parameters.Firstly, we consider the extended growth curve model with a linearly structured covariance matrix. In general there is no problem to estimate the covariance matrix when it is completely unknown. However, problems arise when one has to take into account that there exists a structure generated by a few number of parameters. An estimation procedure that handles linear structured covariance matrices is proposed. The idea is first to estimate the covariance matrix when it may be used to define an inner product in a regression space and thereafter re-estimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed.Secondly, we study a bilinear regression model with matrix normally distributed random errors. For those models, the dispersion matrix follows a Kronecker product structure and it can be used, for example, to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations, a flip-flop relation, are established.At last, the models based on normally distributed random third order tensors are studied. These models are useful in analyzing 3-dimensional data arrays. The 3-dimensional data arrays may be obtained when, for example, a single response is sampled in a 3-D space or in a 2-D space and time, multiple responses are recorded in a 2-D space or in a 1-D space and time. In some studies the analysis is done using the tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker structure. Little attention...

show abstract

Properties of the explicit estimators in the extended growth curve model

Cited by 8 publications

References 14 publications

Estimation for an additive growth curve model with orthogonal design matrices

Estimation for an additive growth curve model with orthogonal design matrices

Maximum likelihood estimators for extended growth curve model with orthogonal between-individual design matrices

Bilinear and Trilinear Regression Models with Structured Covariance Matrices

Contact Info

Product

Resources

About