Analysis of fixed and mixed effects linear models under heteroscedasticity

In this thesis we develop statistical inferential procedures for parameters of linear regression models subject to heteroscedasticity. Such models may arise in the analysis of groups of independent experiments where experiments are repeated at different locations or at different times and it is considered unreasonable to assume the variability at each location or time is the same. In fact, in some cases an experimenter may believe a priori that the variability is subject to a linear order restriction.;Two general problems are considered in this thesis; (a) tests of hypotheses for detecting linear inequalities among the error variances, and (b) point estimation of parameters of the linear model when the error variances are subject to linear inequality restrictions. We address these issues for both fixed effects and mixed effects linear models.;It is shown that no locally best invariant (LBI) test exists for detecting linear inequalities among the error variances when there are more than two groups. On the contrary, the LBI test is derived for the case of two groups. Iterative algorithms are provided for both fixed effects and mixed effects models to obtain point estimates of all the parameters of the model under an assumed order restriction on the error variances. It is shown that these iterative procedures converge.;Additionally we extend previous work concerning inference on the common regression parameter, b , to the mixed effects case. We propose an estimator for b and an estimator of its variance-covariance matrix. Conditions for the consistency of the estimated variance-covariance matrix are determined. We provide examples of consistent estimators in the heteroscedastic case and examples of models satisfying the sufficient conditions. Finally we present some applications to illustrate the methodology developed in this thesis.