| Title:
|
Stability of invariant linearly sufficient statistics in the general Gauss-Markov model (English) |
| Author:
|
Kornacki, Andrzej |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
71-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessary and sufficient conditions are derived for the inclusions $J_0\subset J$ and $J_0^{*}\subset J^{*}$ to be fulfilled where $J_0$, $J_0^{*}$ and $J$, $J^{*}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $GM_0=(y,X_0\beta _0,\sigma _0^2V_0)$ and $GM=(y,X\beta ,\sigma ^2V)$, respectively. (English) |
| Keyword:
|
Gauss-Markov model |
| Keyword:
|
linearly sufficient statistics |
| Keyword:
|
invariant linearly sufficient statistics |
| MSC:
|
62A01 |
| MSC:
|
62B05 |
| MSC:
|
62F10 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 0898.62003 |
| idMR:
|
MR1426681 |
| DOI:
|
10.1023/A:1022244727376 |
| . |
| Date available:
|
2009-09-22T17:53:37Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134345 |
| . |
| Reference:
|
[1] J.K. Baksalary, T. Mathew: Linear sufficiency and completeness in an incorrectly specified general Gauss-Markov model.Sankhyā, Ser A. 48 (1986), 169–180. MR 0905457 |
| Reference:
|
[2] H. Drygas: Sufficiency and completeness in the general Gauss-Markoff model.Sankhyā, Ser A. 45 (1983), 88–98. MR 0749356 |
| Reference:
|
[3] R. Kala: Projectors and linear estimation in general linear models.Comm. Statistics—A, Theory Methods 10 (1981), 849–873. Zbl 0465.62060, MR 0625196, 10.1080/03610928108828078 |
| Reference:
|
[4] T. Mathew, P. Bhimasankaram: Optimality of BLUE$^{\prime }s$ in a general linear model with an incorrect design matrix.J. Statist Plann. Inference 8 (1983), 315–329. MR 0729248, 10.1016/0378-3758(83)90048-4 |
| Reference:
|
[5] W. Oktaba, A. Kornacki, J. Wawrzosek: Invariant linearly sufficient transformations of the general Gauss-Markoff model.Scand. J Statist. 15 (1988), 117–124. MR 0968158 |
| Reference:
|
[6] C.R. Rao: Unified theory of linear estimation.Sankhyā A 35 (1971), 371–394. Zbl 0236.62048, MR 0319321 |
| Reference:
|
[7] C.R. Rao, S.K. Mitra: Generalized Inverse of Matrices and its Applications.Wiley, New York, 1971. MR 0338013 |
| . |
