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Difference based Ridge and Liu type Estimators in Semiparametric Regression Models

  • Esra Akdeniz Duran
  • Wolfgang Karl Härdle
  • Maria Osipenko

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y = Xβ + f + ε. Both estimators are analysed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-014.

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Length: 25 pages
Date of creation: Mar 2011
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2011-014
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  1. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
  2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  3. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
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  6. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521812832.
  7. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
  8. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
  9. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
  11. Hu Yang & Jianwen Xu, 2009. "An alternative stochastic restricted Liu estimator in linear regression," Statistical Papers, Springer, vol. 50(3), pages 639-647, June.
  12. Gülin Tabakan & Fikri Akdeniz, 2010. "Difference-based ridge estimator of parameters in partial linear model," Statistical Papers, Springer, vol. 51(2), pages 357-368, June.
  13. You, Jinhong & Chen, Gemai & Zhou, Yong, 2007. "Statistical inference of partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1539-1557, September.
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