On the principle of MINQUE for the estimation of variance and covariance components

In this thesis, we describe the method of MINQUE (C. R. Rao (1970)) and its various generalizations (C. R. Rao (1971, 1972), Chaubey (1977), P. S. R. S. Rao and Chaubey (1978)). This method can be used if some information about the variance components is available in the form of an a priori guess. Chaubey (1977) outlines the extension for estimating the elements of a covariance matrix using this principle. The method extends easily for the case when no a priori guess of the covariance matrix is assumed. However, for incorporating the a priori guess for estimating the distinct elements of a covariance matrix, we may need to consider a related but different minimization problem, whose solution is provided. A special case of the general model is considered for the numerical illustration