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A new stochastic restricted biased estimator under heteroscedastic or correlated error

Published online by Cambridge University Press:  22 February 2011

Mustafa Ismaeel Alheety
Mustafa Ismaeel Alheety*
Affiliation:
Department of Mathematics, Al-Anbar University, Ramadi, Iraq; alheety@yahoo.com

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. Papers 50 (2007) 639–647] are examined in terms of matrix mean square error criterion. A numerical example is considered to illustrate the theoretical results.

Keywords

Heteroscedasticitygeneralized least squares estimatorstochastic restricted Liu estimator

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011, pp. 30 - 40
Copyright
© EDP Sciences, SMAI, 2011

References

Bayhan, G.M. and Bayhan, M., Forcasting using autocorrelated errors and multicollinear predictor variables. Comput. Ind. Eng. 34 (1998) 413–421. CrossRef
Farebrother, R.W., Fruther results on the mean square error of ridge regression. J. R. Stat. Soc. B 38 (1976) 284–250.
Firinguetti, L., A simulation study of ridge regression estimators with autocorrelated errors. Commun. Stat. Simul. 18 (1989) 673–702. CrossRef
Hoerl, A.E. and Kennard, R.W., Ridge Regression: Biased estimation for non-orthogonal problem. Technometrics 12 (1970) 55–67. CrossRef
Hoerl, A.E. and Kennard, R.W., Ridge Regression: Application for non-orthogonal problem. Technometrics 12 (1970) 69–82. CrossRef
Hubert, M.H. and Wijekoon, P., Improvement of the Liu estimator in linear regression model. Statist. Papers 47 (2006) 471–479. CrossRef
Liu, K., A new class of biased estimate in linear regression. Commun. Stat. – Theory Meth. 22 (1993) 393–402.
C.R. Rao, Linear Statistics Inference and its applications. Second edn. John Wiley and Sons (1973).
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).
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.
Theil, H., On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58 (1963) 401–414. CrossRef
Theil, H. and Goldberger, A.S., On pure and mixed estimation in econometrics. Int. Econ. Rev. 2 (1961) 65–78. CrossRef
Trenkler, G., On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. J. Econometrics 25 (1984) 179–190. CrossRef
Yang, H. and An, J. Xu alternative stochastic restricted Liu estimator in linear regression. Statist. Papers 50 (2007) 639–647. CrossRef