STATISTICAL INFERENCE IN CASE OF ORDER RESTRICTED MIXED MODELS

Abstract

Order-restricted statistical inference is a fertile area of research, structures involving orderings and inequalities increase the efficiency of statistical inferences procedures, and are easy to interpret and apply. The statistical theory under order restrictions has been developed for linear random models. For mixed models, Pan and Khattree (1999) gave a method for estimation in randomized complete block design, which is a special case of mixed models.

The main purpose of this Thesis is to introduce a general review of the order restricted inference on linear models. Moreover, we derive the maximum likelihood estimators for parameters in balanced mixed models under order restrictions. To find these estimators, we need to the formula for the inverse of the covariance matrix. Hocking (1984) gave a structure for the covariance matrix, in which the inverse is easily obtained. We use this structure to derive a method of • estimation in balanced mixed models under order restricted. This

method is used to estimate the parameters of models such as the two­ way mixed model with interaction, randomized complete block design and split-plot model. This work is new and is a generalization of the work done by Pan and Khattree (1999). The computer package used throughout the Thesis IS

Mathematica (Ver 3.1). This package is very helpful for calculating the tedious matrices operations appeared in Chapter V.