A new stochastic restricted biased estimator under heteroscedastic or correlated error

Mustafa Ismaeel Alheety

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page 30-40
  • ISSN: 1292-8100

Abstract

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In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers50 (2007) 639–647] are examined in terms of matrix mean square error criterion. A numerical example is considered to illustrate the theoretical results.

How to cite

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Alheety, Mustafa Ismaeel. "A new stochastic restricted biased estimator under heteroscedastic or correlated error." ESAIM: Probability and Statistics 15 (2011): 30-40. <http://eudml.org/doc/197728>.

@article{Alheety2011,
abstract = { In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers50 (2007) 639–647] are examined in terms of matrix mean square error criterion. A numerical example is considered to illustrate the theoretical results.},
author = {Alheety, Mustafa Ismaeel},
journal = {ESAIM: Probability and Statistics},
keywords = {Heteroscedasticity; generalized least squares estimator; stochastic restricted Liu estimator; heteroscedasticity},
language = {eng},
month = {2},
pages = {30-40},
publisher = {EDP Sciences},
title = {A new stochastic restricted biased estimator under heteroscedastic or correlated error},
url = {http://eudml.org/doc/197728},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Alheety, Mustafa Ismaeel
TI - A new stochastic restricted biased estimator under heteroscedastic or correlated error
JO - ESAIM: Probability and Statistics
DA - 2011/2//
PB - EDP Sciences
VL - 15
SP - 30
EP - 40
AB - In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers50 (2007) 639–647] are examined in terms of matrix mean square error criterion. A numerical example is considered to illustrate the theoretical results.
LA - eng
KW - Heteroscedasticity; generalized least squares estimator; stochastic restricted Liu estimator; heteroscedasticity
UR - http://eudml.org/doc/197728
ER -

References

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  6. M.H. Hubert and P. Wijekoon, Improvement of the Liu estimator in linear regression model. Statist. Papers47 (2006) 471–479.  Zbl1125.62055
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  9. C.R. Rao, H. Toubtenburg and S.C. Heumann, Linear Models and Generalizations: Least squares and alternatives. Springer Ser. Statist. Springer-Verlag, New York (2008).  
  10. C. Stein, Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, in Proc. Third Berkeley Symp. on Mathematics, Statistics and Probability. Universiy of California, Berkeley, 1956, pp. 197–206.  Zbl0073.35602
  11. H. Theil, On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58 (1963) 401–414.  Zbl0129.11401
  12. H. Theil and A.S. Goldberger, On pure and mixed estimation in econometrics. Int. Econ. Rev.2 (1961) 65–78.  
  13. G. Trenkler, On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. J. Econometrics25 (1984) 179–190.  Zbl0559.62054
  14. H. Yang and J. Xu, An alternative stochastic restricted Liu estimator in linear regression. Statist. Papers50 (2007) 639–647.  Zbl1312.62093

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