| Title:
|
A sufficient condition for admissibility in linear estimation (English) |
| Author:
|
Stępniak, Czesław |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1988 |
| Pages:
|
291-295 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
It was recently shown that all estimators which are locally best in the relative interior of the parameter set, together with their limits constitute a complete class in linear estimation, both unbiased and biased. However, not all these limits are admissible. A sufficient condition for admissibility of a limit was given by the author (1986) for the case of unbiased estimation in a linear model with the natural parameter space. This paper extends this result to the general linear model and to biased estimation. (English) |
| Keyword:
|
sufficient condition for admissibility |
| Keyword:
|
natural parameter space |
| Keyword:
|
general linear model |
| Keyword:
|
biased estimation |
| MSC:
|
62C15 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 0665.62012 |
| idMR:
|
MR0949250 |
| DOI:
|
10.21136/AM.1988.104310 |
| . |
| Date available:
|
2008-05-20T18:34:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104310 |
| . |
| Reference:
|
[1] C. R. Blyth: On minimax statistical decision procedures and their admissibility.Ann. Math. Statist. 22 (1951), 22-44. Zbl 0042.38303, MR 0039966, 10.1214/aoms/1177729690 |
| Reference:
|
[2] A. Cohen: All admissible linear estimates of the mean vector.Ann. Math. Statist. 37 (1966), 458-463. Zbl 0146.40201, MR 0189164, 10.1214/aoms/1177699528 |
| Reference:
|
[3] L. R. LaMotte: Admissibility in linear estimation.Ann. Statist. 10 (1982), 245-255. Zbl 0485.62070, MR 0642736, 10.1214/aos/1176345707 |
| Reference:
|
[4] 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:
|
[5] C. R. Rao: Estimation of parameters in a linear model.Ann. Statist. 4 (1976), 1023-1037. Zbl 0336.62055, MR 0420979, 10.1214/aos/1176343639 |
| Reference:
|
[6] R. T. Rockafellar: Convex Analysis.Princeton Univ. Press, 1970. Zbl 0193.18401, MR 0274683 |
| Reference:
|
[7] N. Shinozaki: A study of generalized inverse of matrix and estimation with quadratic loss.Ph. D. Thesis, Keio University, 1975. |
| Reference:
|
[8] C. Stępniak: On admissible estimators in a linear model.Biom. J. 7 (1984), 815-816. MR 0775200, 10.1002/bimj.4710260725 |
| Reference:
|
[9] C. Stępniak: Admissible linear estimators in a linear model with the natural parameter space.Bull. Informatics and Cybernetics. 22 (1986), 71 - 77. MR 0853590, 10.5109/13378 |
| Reference:
|
[10] C. Stępniak: A complete class for linear estimation in a general linear model.Ann. Inst. Statist. Math. A. 39 (1987), 563-573. MR 0930530, 10.1007/BF02491490 |
| . |
