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Journal of Applied Mathematics
Volume 2014, Article ID 639070, 6 pages
http://dx.doi.org/10.1155/2014/639070
Research Article

Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

Department of Statistics and Actuarial Science, Chongqing University, Chongqing 401331, China

Received 15 January 2014; Accepted 8 March 2014; Published 2 April 2014

Academic Editor: Li Weili

Copyright © 2014 Yalian Li and Hu Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. F. Massy, “Principal components regression in exploratory statistical research,” The Journal of the American Statistical Association, vol. 60, no. 309, pp. 234–266, 1965. View at Google Scholar
  2. A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems,” Technometrics, vol. 42, no. 1, pp. 80–86, 2000. View at Google Scholar · View at Scopus
  3. K. J. Liu, “A new class of biased estimate in linear regression,” Communications in Statistics—Theory and Methods, vol. 22, no. 2, pp. 393–402, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  4. B. Singh, Y. P. Chaubey, and T. D. Dwivedi, “An almost unbiased ridge estimator,” Sankhyā. The Indian Journal of Statistics. Series B, vol. 48, no. 3, pp. 342–346, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. F. Akdeniz and S. Kaçıranlar, “On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE,” Communications in Statistics—Theory and Methods, vol. 24, no. 7, pp. 1789–1797, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Kaçıranlar, S. Sakallioğlu, F. Akdeniz, G. P. H. Styan, and H. J. Werner, “A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland cement,” Sankhyā. The Indian Journal of Statistics. Series B, vol. 61, pp. 443–459, 1999. View at Google Scholar
  7. F. Akdeniz and H. Erol, “Mean squared error matrix comparisons of some biased estimators in linear regression,” Communications in Statistics—Theory and Methods, vol. 32, no. 12, pp. 2389–2413, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. H. Hubert and P. Wijekoon, “Improvement of the Liu estimator in linear regression model,” Statistical Papers, vol. 47, no. 3, pp. 471–479, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. R. Baye and D. F. Parker, “Combining ridge and principal component regression: a money demand illustration,” Communications in Statistics—Theory and Methods, vol. 13, no. 2, pp. 197–205, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Kaçıranlar and S. Sakallıoğlu, “Combining the Liu estimator and the principal component regression estimator,” Communications in Statistics—Theory and Methods, vol. 30, no. 12, pp. 2699–2705, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Xu and H. Yang, “On the restricted r-k class estimator and the restricted r-d class estimator in linear regression,” Journal of Statistical Computation and Simulation, vol. 81, no. 6, pp. 679–691, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. B. Wu and H. Yang, “On the stochastic restricted almost unbiased estimators in linear regression model,” Communications in Statistics-Simulation and Computation, vol. 43, pp. 428–440, 2014. View at Google Scholar
  13. J. K. Baksalary and G. Trenkler, “Nonnegative and positive definiteness of matrices modified by two matrices of rank one,” Linear Algebra and Its Applications, vol. 151, pp. 169–184, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. N. Sarkar, “Mean square error matrix comparison of some estimators in linear regressions with multicollinearity,” Statistics & Probability Letters, vol. 30, no. 2, pp. 133–138, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Li and H. Yang, “A new stochastic mixed ridge estimator in linear regression model,” Statistical Papers, vol. 51, no. 2, pp. 315–323, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet