In this paper, we consider the general growth curve model with multivariate random effects covariance structure and provide a new simple estimator for the parameters of interest. This estimator is not only convenient for testing the hypothesis on the corresponding parameters, but also has higher...

This paper establishes a type of Kantorovich inequality subject to some constraints and obtains some lower bounds for the relative efficiency of the least squares. These lower bounds can be much sharper than that obtained by using the unconstrained Kantorovich inequality. Multivariate extensions...

Estimation of parameters in the classical Growth Curve model, when the covariance matrix has some specific linear structure, is considered. In our examples maximum likelihood estimators cannot be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are...

An extended growth curve model is considered which, among other things, is useful when linear restrictions exist on the mean in the ordinary growth curve model. The maximum likelihood estimators consist of complicated stochastic expressions. It is shown how, by the aid of fairly elementary...

Likelihood ratio tests for detecting a single outlier in multivariate linear models are considered, where an observation is called an outlier if there has been a shift in the mean. The test statistics are the maximum of n nonindependent statistics, where n is the number of observations. Relevant...

A unified approach of treating multivariate linear normal models is presented. The results of the paper are based on a useful extension of the growth curve model. In particular, the finding of maximum likelihood estimators when linear restrictions exist on the parameters describing the mean in...

This paper is concerned with an extended growth curve model with two within-individual design matrices which are hierarchically related. For the model some random-coefficient covariance structures are reduced. LR tests for testing the adequacy of each of these random-coefficient structures and...

In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. A trilinear example is used to explain the...

A trace test for the mean parameters of the growth curve model is proposed. It is constructed using the restricted maximum likelihood followed by an estimated likelihood ratio approach. The statistic reduces to the Lawley-Hotelling trace test for the Multivariate Analysis of Variance (MANOVA)...

This article analyzes whether some existing tests for the pxp covariance matrix [Sigma] of the N independent identically distributed observation vectors work under non-normality. We focus on three hypotheses testing problems: (1) testing for sphericity, that is, the covariance matrix [Sigma] is...