Estimation for an additive growth curve model with orthogonal design matrices

Hu, Jianhua; Yan, Guohua; You, Jinhong

doi:10.3150/10-bej315

Cited by 8 publications

(2 citation statements)

References 24 publications

(34 reference statements)

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“…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

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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...

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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

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“…For example in [5] the explicit MLEs are presented with the nested subspace conditions on the within design matrices instead. In [6,7] the extended growth curve model without nested subspace conditions but with orthogonal design matrices is considered and generalized leastsquares estimators and their properties are studied.…”

Section: Introductionmentioning

confidence: 99%

Extended GMANOVA model with a linearly structured covariance matrix

2015

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In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1 orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied.

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Space Decomposition and Estimation in Multivariate Linear Models

Nzabanita

Ngaruye

2020

Recent Developments in Multivariate and Random Matrix Analysis

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Estimation for an additive growth curve model with orthogonal design matrices

Cited by 8 publications

References 24 publications

Bilinear and Trilinear Regression Models with Structured Covariance Matrices

Bilinear and Trilinear Regression Models with Structured Covariance Matrices

Extended GMANOVA model with a linearly structured covariance matrix

Space Decomposition and Estimation in Multivariate Linear Models

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