Nada Mohamed Nabil Mohamed Elmaamon Mohamed Denana <br/><br/>
The use of least square method of estimating variance components in linear models /  
 استحدام طريقة المربعات الصغري في تقدير مكونات التباين في النماذج الخطية  
Nada Mohamed Nabil Mohamed Elmaamon Mohamed Denana ; Supervised Elhoussainy Abdelbar Rady 
 - Cairo :   Nada Mohamed Nabil Mohamed Elmaamon Mohamed Denana ,   2018 
 - 75 Leaves ;   30cm  
<br/><br/>Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Statistics and Econometrics 
<br/><br/> There exist many different methods for variance component estimation. The methods differ in the estimation principle employed, as well as in the distributional assumptions that need to be made. Most methods have been devised for the linear model, for which one assumes that the covariance matrix of the observables can be written as an unknown linear combination of known cofactor matrices. The coefficients of this linear combination are then the unknown (co)variance components that need to be estimated. In the first part of this dissertation, some of methods for variance component estimation will be presented like the minimum norm quadratic unbiased estimator (MINQUE), Henderson, the best invariant quadratic unbiased estimator (BIQUE), the maximum likelihood, ANOVA method, and the Minimum variance quadratic unbiased estimator (MIVQUE). In the second part of this dissertation, the method of weighted least-squares variance component estimation will be studied, and an elaboration on theoretical and practical aspects of the method will be given. The WLS-VCE will be shown to be a simple, flexible, and attractive VCE-method. The method is studied for two classes of weight matrices: a general weight matrix and a weight matrix from the unit weight matrix class. Finally, a simulation study will be conducted to make a comparison study between weighted least square method and maximum likelihood method, MINQUE method, BIQUE method, MIVQUE method and least square method to estimate variance components in linear model under different sample size 
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<br/><br/><label>Subjects--Index Terms: </label>Estimating variance components Least square method Linear models