# A new stochastic restricted biased estimator under heteroscedastic or correlated error

ESAIM: Probability and Statistics (2011)

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

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topAlheety, 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/277160>.

@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. 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.},

author = {Alheety, Mustafa Ismaeel},

journal = {ESAIM: Probability and Statistics},

keywords = {heteroscedasticity; generalized least squares estimator; stochastic restricted Liu estimator},

language = {eng},

pages = {30-40},

publisher = {EDP-Sciences},

title = {A new stochastic restricted biased estimator under heteroscedastic or correlated error},

url = {http://eudml.org/doc/277160},

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

PY - 2011

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. 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.

LA - eng

KW - heteroscedasticity; generalized least squares estimator; stochastic restricted Liu estimator

UR - http://eudml.org/doc/277160

ER -

## References

top- [1] G.M. Bayhan and M. Bayhan, Forcasting using autocorrelated errors and multicollinear predictor variables. Comput. Ind. Eng.34 (1998) 413–421.
- [2] R.W. Farebrother, Fruther results on the mean square error of ridge regression. J. R. Stat. Soc. B38 (1976) 284–250. Zbl0344.62056MR653156
- [3] L. Firinguetti, A simulation study of ridge regression estimators with autocorrelated errors. Commun. Stat. Simul.18 (1989) 673–702. Zbl0695.62176MR1016233
- [4] A.E. Hoerl and R.W. Kennard, Ridge Regression: Biased estimation for non-orthogonal problem. Technometrics12 (1970) 55–67. Zbl0202.17205
- [5] A.E. Hoerl and R.W. Kennard, Ridge Regression: Application for non-orthogonal problem. Technometrics12 (1970) 69–82. Zbl0202.17206
- [6] M.H. Hubert and P. Wijekoon, Improvement of the Liu estimator in linear regression model. Statist. Papers47 (2006) 471–479. Zbl1125.62055MR2276209
- [7] K. Liu, A new class of biased estimate in linear regression. Commun. Stat. – Theory Meth.22 (1993) 393–402. Zbl0784.62065MR1212418
- [8] C.R. Rao, Linear Statistics Inference and its applications. Second edn. John Wiley and Sons (1973). Zbl0256.62002MR346957
- [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). Zbl1151.62063MR2370506
- [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. Zbl0073.35602MR84922
- [11] H. Theil, On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc.58 (1963) 401–414. Zbl0129.11401MR149612
- [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. Zbl0559.62054MR748043
- [14] H. Yang and J. Xu, An alternative stochastic restricted Liu estimator in linear regression. Statist. Papers50 (2007) 639–647. Zbl1312.62093MR2507842

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