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rk Class estimator in the linear regression model with correlated errors

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Abstract

Autocorrelation in errors and multicollinearity among the regressors are serious problems in regression analysis. The aim of this paper is to examine multicollinearity and autocorrelation problems concurrently and to compare the rk class estimator to the generalized least squares estimator, the principal components regression estimator and the ridge regression estimator by the scalar and matrix mean square error criteria in the linear regression model with correlated errors.

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References

  • Aitken AC (1935) On least squares and linear combinations of observations. Proc R Soc Edinb 55: 42–48

    Google Scholar 

  • Baye MR, Parker DF (1984) Combining ridge and principal component regression: a money demand illustration. Commun Stat Theory Methods 13: 197–205

    Article  MathSciNet  Google Scholar 

  • Bayhan GM, Bayhan M (1998) Forecasting using autocorrelated errors and multicollinear predictor variables. Comp Ind Eng 34(2): 413–421

    Article  Google Scholar 

  • Farebrother RW (1976) Further results on the mean square error of ridge regression. J R Stat Soc Ser B Methodol 38(3): 248–250

    MATH  MathSciNet  Google Scholar 

  • Firinguetti L (1989) A simulation study of ridge regression estimators with autocorrelated errors. Commun Stat Simul 18(2): 673–702

    Article  MATH  Google Scholar 

  • Graybill FA (1976) Theory and application of the linear model. Duxbury Press, Pacific Grove

    MATH  Google Scholar 

  • Griffiths WE, Hill RC, Judge GC (1993) Learning and practicing econometrics. Wiley, New York

    Google Scholar 

  • Güler H, Kaçıranlar S (2009) A comparison of mixed and ridge estimators of linear models. Commun Stat Simul Comput 38: 2, 368–401

    Article  Google Scholar 

  • Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12: 55–67

    Article  MATH  Google Scholar 

  • Kibria BMG (2003) Performance of some new ridge regression estimators. Commun Stat Simul Comput 32(2): 419–435

    Article  MATH  MathSciNet  Google Scholar 

  • McDonald GC, Galarneau DI (1975) A monte carlo evaluation of some ridge-type estimators. J Am Stat Assoc 20: 407–416

    Article  Google Scholar 

  • Nomura M, Ohkubo T (1985) A note on combining ridge and principal component regression. Commun Stat Theory Methods 14: 2489–2493

    Article  MATH  MathSciNet  Google Scholar 

  • Obenchain RL (1975) Ridge analysis following a preliminary test of the shrunken hypothesis. Technometrics 17: 431–445

    Article  MATH  MathSciNet  Google Scholar 

  • Sarkar N (1996) Mean square error matrix comparison of some estimators in linear regressions with multicollinearity. Stat Probab Lett 30: 133–138

    Article  MATH  Google Scholar 

  • Trenkler G (1984) On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. J Econom 25: 179–190

    Article  MATH  MathSciNet  Google Scholar 

  • Trenkler G, Trenkler D (1983) A note on superiority comparisons of homogeneous linear estimators. Commun Stat A Theory Methods 12(7): 799–808

    Article  MATH  MathSciNet  Google Scholar 

  • Trenkler G, Toutenburg H (1990) Mean squared error matrix comparisons between biased estimators: an overview of recent results. Stat Papers 31(3): 165–179

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Gülesen Üstündagˇ Şiray.

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Üstündagˇ Şiray, G., Kaçıranlar, S. & Sakallıoğlu, S. rk Class estimator in the linear regression model with correlated errors. Stat Papers 55, 393–407 (2014). https://doi.org/10.1007/s00362-012-0484-8

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  • DOI: https://doi.org/10.1007/s00362-012-0484-8

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