| Title:
|
Estimation of variance components in mixed linear models (English) |
| Author:
|
Volaufová, Júlia |
| Author:
|
Witkovský, Viktor |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
139-148 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The MINQUE of the linear function $\int'\vartheta$ of the unknown variance-components parameter $\vartheta$ in mixed linear model under linear restrictions of the type $\bold R\vartheta = c$ is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions $\vartheta_1 = k\vartheta_2$, where $k \geq 0$, is given. (English) |
| Keyword:
|
minimum invariant quadratic estimators |
| Keyword:
|
MINQUE |
| Keyword:
|
mixed linear model |
| Keyword:
|
linear restrictions |
| Keyword:
|
one-way classification model |
| MSC:
|
62F10 |
| MSC:
|
62J05 |
| MSC:
|
62J10 |
| idZBL:
|
Zbl 0746.62066 |
| idMR:
|
MR1149163 |
| DOI:
|
10.21136/AM.1992.104497 |
| . |
| Date available:
|
2008-05-20T18:43:19Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104497 |
| . |
| Reference:
|
[1] C. R. Rao: Estimation of variance and covariance components - MINQUE theory.Journal of Multivariate Analysis 1 (1971), 267-275. Zbl 0223.62086, MR 0301869 |
| Reference:
|
[2] C. R. Rao, J. Kleffe: Estimation of Variance Components and Applications.volume 3 of Statistics and probability, North-Holland, Amsterdam, New York, Oxford, Tokyo, 1988, first edition. Zbl 0645.62073, MR 0933559 |
| Reference:
|
[3] C. R. Rao, S. K. Mitra: Generalized Inverse of Matrices and Its Applications.John Wiley & Sons, New York, London, Sydney, Toronto, 1971, first edition. Zbl 0236.15005, MR 0338013 |
| Reference:
|
[4] J. Seely: Linear spaces and unbiased estimation.Ann. Math. Stat. 41 (1970), 1725-1734. Zbl 0263.62041, MR 0275559, 10.1214/aoms/1177696817 |
| Reference:
|
[5] L. R. Verdooren: Practical aspects of variance component estimation.invited lecture for the 4th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis Mülhausen, GDR, May 1979. |
| Reference:
|
[6] G. Zyskind: On canonical forms, negative covariance matrices and best and simple least square estimator in linear models.Ann. Math. Stat. 38 (1967), 1092-1110. MR 0214237, 10.1214/aoms/1177698779 |
| . |
