Accession Number : AD0720715

Title :   Mixed Effects Model Estimation - Optimal Properties.

Descriptive Note : Technical memo.,

Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK ORDNANCE RESEARCH LAB

Personal Author(s) : Atzinger,Erwin M.

Report Date : 20 JUL 1970

Pagination or Media Count : 99

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)

Descriptors :   (*MODEL THEORY, EXPERIMENTAL DESIGN), (*STATISTICAL ANALYSIS, DECISION THEORY), COMBINATORIAL ANALYSIS, MATRICES(MATHEMATICS), OPTIMIZATION, THEOREMS, THESES

Subject Categories : Statistics and Probability
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE