| Title:
|
On admissibility of linear estimators in models with finitely generated parameter space (English) |
| Author:
|
Synówka-Bejenka, Ewa |
| Author:
|
Zontek, Stefan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2016 |
| Pages:
|
724-734 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper refers to the research on the characterization of admissible estimators initiated by Cohen [2]. In our paper it is proved that for linear models with finitely generated parameter space the limit of a sequence of the unique locally best linear estimators is admissible. This result is used to give a characterization of admissible linear estimators of fixed and random effects in a random linear model for spatially located sensors measuring intensity of a source of signals in discrete instants of time. (English) |
| Keyword:
|
linear model |
| Keyword:
|
linear estimation |
| Keyword:
|
linear prediction |
| Keyword:
|
admissibility |
| Keyword:
|
admissibility among an affine set |
| Keyword:
|
locally best estimator |
| MSC:
|
62F10 |
| MSC:
|
62J10 |
| idZBL:
|
Zbl 06674936 |
| idMR:
|
MR3602012 |
| DOI:
|
10.14736/kyb-2016-5-0724 |
| . |
| Date available:
|
2017-01-02T13:26:35Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145965 |
| . |
| Reference:
|
[1] Baksalary, J. K., Markiewicz, A.: Admissible linear estimators in the general Gauss-Markov model..J. Statist. Plann. Inference 19 (1988), 349-359. Zbl 0656.62076, MR 0955399, 10.1016/0378-3758(88)90042-0 |
| Reference:
|
[2] Cohen, A.: All admissible estimates of the mean vector..Ann. Math. Statist. 37 (1966), 458-463. MR 0189164, 10.1214/aoms/1177699528 |
| Reference:
|
[3] Gnot, S., Kleffe, J.: Quadratic estimation in mixed linear models with two variance components..J. Statist. Plann. Inference 8 (1983), 267-279. Zbl 0561.62064, MR 0729245, 10.1016/0378-3758(83)90045-9 |
| Reference:
|
[4] Gnot, S., Rafajłowicz, E., Urbańska-Motyka, A.: Statistical inference in linear model for spatially located sensors and random inputs..Ann. Inst. Statist Math. 53 (2001), 370-379. MR 1841142, 10.1023/a:1012426923971 |
| Reference:
|
[5] Goldberger, A. S.: Best linear unbiased prediction in the generalized linear regression model..J. Amer. Statist. Assoc. 57 (1962), 369-375. Zbl 0124.35502, MR 0143295, 10.1080/01621459.1962.10480665 |
| Reference:
|
[6] Gro{\ss}, J., Markiewicz, A.: Characterization of admissible linear estimators in the linear model..Linear Algebra Appl. 388 (2004), 239-248. MR 2077862, 10.1016/s0024-3795(03)00459-2 |
| Reference:
|
[7] Harville, D. A.: Extension of the Gauss-Markov theorem to include the estimation of random effects..Ann. Statist. 2 (1976), 384-395. Zbl 0323.62043, MR 0398007, 10.1214/aos/1176343414 |
| Reference:
|
[8] Henderson, C. R.: Estimation of genetic parameters (abstract)..Ann. Math. Statist. 21 (1950), 309-310. |
| Reference:
|
[9] Henderson, C. R.: Selection index and expected genetic advance..In: Statistical Genetics and Plant Breeding (W. D. Hanson and H. F. Robinson, eds.), NAS-NRC 982, Washington 1963, pp. 141-163. |
| Reference:
|
[10] Jiang, J.: A derivation of BLUP-Best linear unbiased predictor..Statist. Probab. Lett. 32 (1997), 321-324. Zbl 0886.62066, MR 1440842, 10.1016/s0167-7152(96)00089-2 |
| Reference:
|
[11] Klonecki, W., Zontek, S.: On the structure of admissible linear estimators..J. Multivariate Anal. 24 (1988), 11-30. Zbl 0664.62008, MR 0925126, 10.1016/0047-259x(88)90098-x |
| Reference:
|
[12] LaMotte, L. R.: Admissibility in linear estimation..Ann. Statist. 10 (1982), 245-255. Zbl 0485.62070, MR 0642736, 10.1214/aos/1176345707 |
| Reference:
|
[13] LaMotte, L. R.: On limits of uniquely best linear estimators..Metrika 45 (1997), 197-211. MR 1452063, 10.1007/bf02717103 |
| Reference:
|
[14] Liu, X. Q., Rong, J. Y., Liu, X. Y.: Best linear unbiased prediction for linear combinations in general mixed linear models..J. Multivariate Anal. 99 (2008), 1503-1517. Zbl 1144.62047, MR 2444809, 10.1016/j.jmva.2008.01.004 |
| Reference:
|
[15] Olsen, A., Seely, J., Birkes, D.: Invariant quadratic unbiased estimation for two variance components..Ann. Statist. 4 (1976), 878-890. Zbl 0344.62060, MR 0418345, 10.1214/aos/1176343586 |
| Reference:
|
[16] Rao, C. R.: Estimation of parameters in a linear model..Ann. Statist. 4 (1976), 1023-1037. Zbl 0421.62047, MR 0420979, 10.1214/aos/1176343639 |
| Reference:
|
[17] Rao, C. R.: Estimation in linear models with mixed effects: a unified theory..In: Proc. Second International Tampere Conference in Statistics (T. Pukkila and S. Puntanen, eds.), Dept. of Mathematical Sciences, Univ. of Tampere, Tampere 1987, pp. 73-98. |
| Reference:
|
[18] Robinson, G. K.: That BLUP is a good thing-the estimation of random effects..Statist. Sci. 6 (1991), 15-51. Zbl 0955.62500, MR 1108815, 10.1214/ss/1177011933 |
| Reference:
|
[19] Shiqing, W., Ying, M., Zhijun, F.: Integral expression form of admissible linear estimators of effects in linear mixed models..In: Proc. 2010 International Conference on Computing, Control and Industrial Engineering, IEEE, Wuhan 2010, pp. 56-60. 10.1109/ccie.2010.133 |
| Reference:
|
[20] Stępniak, C.: On admissible estimators in a linear model..Biometrical J. 26 (1984), 815-816. Zbl 0565.62042, MR 0775200, 10.1002/bimj.4710260725 |
| Reference:
|
[21] Stępniak, C.: A complete class for linear estimation in a general linear model..Ann. Inst. Statist. Math. A 39 (1987), 563-573. Zbl 0691.62010, MR 0930530, 10.1007/bf02491490 |
| Reference:
|
[22] Stępniak, C.: Admissible invariant esimators in a linear model..Kybernetika 50 (2014), 310-321. MR 3245533, 10.14736/kyb-2014-3-0310 |
| Reference:
|
[23] Synówka-Bejenka, E., Zontek, S.: A characterization of admissible linear estimators of fixed and random effects in linear models..Metrika 68 (2008), 157-172. MR 2434311, 10.1007/s00184-007-0149-0 |
| Reference:
|
[24] Tian, Y.: A new derivation of BLUPs under random-effects model..Metrika 78 (2015), 905-918. Zbl 1329.62264, MR 3407588, 10.1007/s00184-015-0533-0 |
| Reference:
|
[25] Zontek, S.: On characterization of linear admissible estimators: an extension of a result due to C. R. Rao..J. Multivariate Anal. 23 (1987), 1-12. Zbl 0647.62062, MR 0911790, 10.1016/0047-259x(87)90174-6 |
| Reference:
|
[26] Zontek, S.: Admissibility of limits of the unique locally best linear estimators with application to variance components models..Probab. Math. Statist. 9 (1988), 29-44. Zbl 0674.62008, MR 0985523 |
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