REML estimation with restricted parameter spaces /
Restricted parameter spaces for covariance matrices, such as [Sigma] = [sigma]^{2}I or [Sigma] = [alpha]I + [beta]J, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to insure that estimates satisfy a priori hypotheses. With multivariate variance comp...
| Main Authors: | , |
|---|---|
| Corporate Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
College Station, Texas :
Department of Statistics, Texas A & M University,
1992.
|
| Series: | Technical report (Texas A & M University. Department of Statistics) ;
no. 176. |
| Subjects: |
| Summary: | Restricted parameter spaces for covariance matrices, such as [Sigma] = [sigma]^{2}I or [Sigma] = [alpha]I + [beta]J, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to insure that estimates satisfy a priori hypotheses. With multivariate variance components models, several covariance matrices need to be simultaneously estimated and even with a reduced parameter space, estimation can be difficult. Calvin and Dykstra (1991-balanced data) and Calvin (1992-unbalanced data) discuss estimation for a widely-used class of models where the variance components matrices need only be nonnegative definite. In this paper, we extend these results to handle a wide class of restricted parameter spaces. The examples listed above are members of this class. We state the conditions required for a parameterization to be a member of the class, discuss the implementation of the results for several different members of the class and discuss estimation with both balanced and unbalanced data. Several examples are also used to demonstrate the results. |
|---|---|
| Item Description: | "Date: 4 June 1992"--Leaf [i]. Funding information taken from leaf [i]. |
| Physical Description: | 19 leaves ; 28 cm |
| Bibliography: | Includes bibliographical references (leaves 17-19). |