The College of Education for Pure Sciences in the Department of Mathematics at the University of Basra has discussed a master’s thesis on statistical inference in variance components
The message presented by the researcher (Ammar Abdel Amir Hamza) included
A study of statistical inference in the variance components of repeated measures models. Three aspects of the work are considered. In the first aspect, we consider the repeated measures model, which has only one factor within units, one factor between units and an interaction factor and includes three univariate random effects in addition to the error term of the model. And we search in the analysis of variance and we also estimated the model parameters using two methods, the first is the least squares method and the second is the greatest weighting method, as well as checking some properties of the estimators, unbiased, consistent, efficient and sufficient, and we found confidence intervals for the variance components of the repeated measures model, and the hypotheses related to the model parameters were tested. Using the weighting ratio test.
 On the other hand, we presented a number of measures of the type
On the linear combinations of variance components in the repeated measures model, we proposed extending these ANOVA procedures to include unbalanced designs by substituting the mean squares.
And we explained how to use this usual mean squares ANOVA with unbalanced squares
New in building confidence intervals on linear sets of variance components, we have also developed a new set of statistics that we can use in building confidence intervals for variance components in the repeated measures model, and these statistics are an alternative to the unweighted generalized mean squares that we obtained previously.
Finally, we selected real data for an experiment to illustrate the practical aspect of the methods used in this study. The aim of the data set is to study the effect of season, plant variety, different levels of sulfur, two different levels of superphosphate and levels of soil leaching process on the height of lettuce plants grown in highly saline environment.
Recommended letter
Study the estimation of variance components in the multivariate repeated measures model, by maximizing and we use a modified method to estimate the parameters of the multivariate repeated measures model at several levels.
Studying the adequacy and completeness of the multivariate repeated measures model by transforming the problem using the orthogonal matrix and finding the minimum unbiased estimators of variance for the model parameters. Studying the Bayesian method on the multivariate repeated measurements model and finding the probability distribution to make inferences on the multivariate repeated measurements model.