| Title:
|
Bayes unbiased estimation in a model with three variance components (English) |
| Author:
|
Stuchlý, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
5 |
| Year:
|
1989 |
| Pages:
|
375-386 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $\bold{t=X\beta + \epsilon}$, $\bold{E(t)=X\beta}$, $\bold {Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given. (English) |
| Keyword:
|
necessary and sufficient conditions for an existence |
| Keyword:
|
Bayes invariant quadratic unbiased estimate |
| Keyword:
|
linear function of variance components |
| Keyword:
|
mixed linear model |
| Keyword:
|
three unknown variance components |
| Keyword:
|
normal case |
| MSC:
|
62F15 |
| MSC:
|
62H12 |
| MSC:
|
62J10 |
| MSC:
|
62J99 |
| idZBL:
|
Zbl 0689.62026 |
| idMR:
|
MR1014078 |
| DOI:
|
10.21136/AM.1989.104365 |
| . |
| Date available:
|
2008-05-20T18:37:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104365 |
| . |
| Reference:
|
[1] S. Gnot J. Kleffe: Quadratic estimation in mixed linear models with two variance components.Journal of Statist. Planning and Inference 8 (1983), 267-279. MR 0729245, 10.1016/0378-3758(83)90045-9 |
| Reference:
|
[2] J. Kleffe R. Pincus: Bayes and best quadratic unbiased estimators for parameters of the covariance matrix in a normal linear model.Math. Operationsf. Statist. 5 (1974), 43 - 67. MR 0341683, 10.1080/02331887408801147 |
| Reference:
|
[3] A. Olsen J. Seely D. Birkes: Invariant quadratic unbiased estimation for two variance components.Ann. Statist. 4 (1976), 878-890. MR 0418345, 10.1214/aos/1176343586 |
| Reference:
|
[4] C. R. Rao: Linear Statistical Inference and Its Applications.2nd ed. J. Wiley, New York 1973. Zbl 0256.62002, MR 0346957 |
| Reference:
|
[5] C. R. Rao: Minimum variance quadratic unbiased estimation of variance components.J. Multivariate Anal. I (1971), 445-456. Zbl 0259.62061, MR 0301870, 10.1016/0047-259X(71)90019-4 |
| Reference:
|
[6] J. Stuchlý: Bayes unbiased estimation in a model with two variance components.Aplikace matematiky 32, No. 2 (1987), 120-130. MR 0885759 |
| Reference:
|
[7] S. Zacks: The Theory of Statistical Inference.J. Wiley, New York, 1971. MR 0420923 |
| . |
