Mixed Effects Model Estimation - Optimal Properties.
Abstract
Optimal point estimation for the general linear mixed effects model has been examined. The approach used is based on the theory of complete minimal sufficient statistics. Restrictions placed on the model in this thesis are far less severe than those imposed in earlier works. The problem has been solved in cases where a complete minimal sufficient statistic is available. This includes various unbalanced designs for which earlier theory is not applicable. In noncomplete cases, however, the problem of minimum variance estimation is still an open problem. Conditions have been obtained concerning the estimability of the parameters in the model. A nonsingular transformation of the observation vector was then used to obtain a vector statistic sufficient for the parameters. This was followed by a study of the distributional properties and dimensionality of this set of statistics. Completeness of the family of joint distributions of the sufficient statistics was also considered. A study of the theory of the simultaneous diagonalization of noncommutative symmetric matrices is included. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 20, 1970
- Accession Number
- AD0720715
Entities
People
- Erwin M. Atzinger
Organizations
- Pennsylvania State University