Geodesic
On admissibility of linear estimators in models with finitely generated parameter space
Kybernetika, Tome 52 (2016) no. 5, pp. 724-734

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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.
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.
DOI : 10.14736/kyb-2016-5-0724
Classification : 62F10, 62J10
Keywords: linear model; linear estimation; linear prediction; admissibility; admissibility among an affine set; locally best estimator 
Synówka-Bejenka, Ewa; Zontek, Stefan. On admissibility of linear estimators in models with finitely generated parameter space. Kybernetika, Tome 52 (2016) no. 5, pp. 724-734. doi: 10.14736/kyb-2016-5-0724
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[1] Baksalary, J. K., Markiewicz, A.: Admissible linear estimators in the general Gauss-Markov model. J. Statist. Plann. Inference 19 (1988), 349-359. | DOI | MR | Zbl

[2] Cohen, A.: All admissible estimates of the mean vector. Ann. Math. Statist. 37 (1966), 458-463. | DOI | MR

[3] Gnot, S., Kleffe, J.: Quadratic estimation in mixed linear models with two variance components. J. Statist. Plann. Inference 8 (1983), 267-279. | DOI | MR | Zbl

[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. | DOI | MR

[5] Goldberger, A. S.: Best linear unbiased prediction in the generalized linear regression model. J. Amer. Statist. Assoc. 57 (1962), 369-375. | DOI | MR | Zbl

[6] Gro{\ss}, J., Markiewicz, A.: Characterization of admissible linear estimators in the linear model. Linear Algebra Appl. 388 (2004), 239-248. | DOI | MR

[7] Harville, D. A.: Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann. Statist. 2 (1976), 384-395. | DOI | MR | Zbl

[8] Henderson, C. R.: Estimation of genetic parameters (abstract). Ann. Math. Statist. 21 (1950), 309-310.

[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.

[10] Jiang, J.: A derivation of BLUP-Best linear unbiased predictor. Statist. Probab. Lett. 32 (1997), 321-324. | DOI | MR | Zbl

[11] Klonecki, W., Zontek, S.: On the structure of admissible linear estimators. J. Multivariate Anal. 24 (1988), 11-30. | DOI | MR | Zbl

[12] LaMotte, L. R.: Admissibility in linear estimation. Ann. Statist. 10 (1982), 245-255. | DOI | MR | Zbl

[13] LaMotte, L. R.: On limits of uniquely best linear estimators. Metrika 45 (1997), 197-211. | DOI | MR

[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. | DOI | MR | Zbl

[15] Olsen, A., Seely, J., Birkes, D.: Invariant quadratic unbiased estimation for two variance components. Ann. Statist. 4 (1976), 878-890. | DOI | MR | Zbl

[16] Rao, C. R.: Estimation of parameters in a linear model. Ann. Statist. 4 (1976), 1023-1037. | DOI | MR | Zbl

[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.

[18] Robinson, G. K.: That BLUP is a good thing-the estimation of random effects. Statist. Sci. 6 (1991), 15-51. | DOI | MR | Zbl

[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. | DOI

[20] Stępniak, C.: On admissible estimators in a linear model. Biometrical J. 26 (1984), 815-816. | DOI | MR | Zbl

[21] Stępniak, C.: A complete class for linear estimation in a general linear model. Ann. Inst. Statist. Math. A 39 (1987), 563-573. | DOI | MR | Zbl

[22] Stępniak, C.: Admissible invariant esimators in a linear model. Kybernetika 50 (2014), 310-321. | DOI | MR

[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. | DOI | MR

[24] Tian, Y.: A new derivation of BLUPs under random-effects model. Metrika 78 (2015), 905-918. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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. | MR | Zbl

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