| Title:
|
Bayes unbiased estimation in a model with two variance components (English) |
| Author:
|
Stuchlý, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1987 |
| Pages:
|
120-130 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model $\bold{t=X\beta+\epsilon}$, $\bold{E(t)=X\beta}$, $\bold{D(t)=0_1U_1+0_2U_2}$ with the unknown variance componets in the normal case. The matrices $\bold{U_1}$, $\bold{U_2}$ may be singular. Applications to two examples of the analysis of variance are given. (English) |
| Keyword:
|
risk function |
| Keyword:
|
explicit expression |
| Keyword:
|
Bayes invariant quadratic unbiased estimate |
| Keyword:
|
linear function of the variance components |
| Keyword:
|
mixed linar model |
| Keyword:
|
normal case |
| MSC:
|
62C15 |
| MSC:
|
62F15 |
| MSC:
|
62J10 |
| MSC:
|
62J99 |
| idZBL:
|
Zbl 0625.62019 |
| idMR:
|
MR0885759 |
| DOI:
|
10.21136/AM.1987.104241 |
| . |
| Date available:
|
2008-05-20T18:31:51Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104241 |
| . |
| Reference:
|
[1] S. Gnot J. Kleffe: Quadratic estimation in mixed linear models with two variance components.Journal of statistical planning and Inference 8 (1983) 267-279. MR 0729245, 10.1016/0378-3758(83)90045-9 |
| Reference:
|
[2] L. Kubáček: Fundaments of the theory of estimates.(Slovak). Veda, Publishing House of Slovak Acad. Sc., Bratislava 1983,. |
| Reference:
|
[3] C. R. Rao: Minimum variance quadratic unbiased estimation of variance components.J. Multivariate Anal. (1971) I, 445-456. Zbl 0259.62061, MR 0301870, 10.1016/0047-259X(71)90019-4 |
| Reference:
|
[4] C. R. Rao: Linear statistical inference and its applications.J. Wiley, New York 1973. Zbl 0256.62002, MR 0346957 |
| Reference:
|
[5] C. R. Rao S. K. Mitra: Generalized inverse of matrices and its applications.J. Wiley, New York 1972. MR 0338013 |
| . |
