Modified Liu-Type Estimator Based on (r − k) Class Estimator

References

• Alheety , M. I. , Gore , S. D. ( 2008 ). A new estimator in multiple linear regression . Model Ass. Statist. Applic. 3 ( 3 ): 187 – 200 .
   Google Scholar
• Baye , M. R. , Parker , D. F. ( 1984 ). Combining ridge and principal component regression . Commun. Statist. Theor. Meth. 13 ( 2 ): 197 – 205 .
   Web of Science ®Google Scholar
• Alkhamisi , M. , Khalaf , G. , Shukur , G. ( 2006 ). Some modifications for choosing ridge parameters . Commun. Statist. Theor. Meth. 35 : 2005 – 2020 .
   Web of Science ®Google Scholar
• Alkhamisi , M. , Shukur , G. ( 2008 ). Developing ridge parameters for SUR model . Commun. Statist. Theor. Meth. 37 ( 4 ): 544 – 564 .
   Web of Science ®Google Scholar
• Alkhamisi , M. ( 2010 ). Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies . Statist. Pap. 51 ( 3 ): 651 – 672 .
   Web of Science ®Google Scholar
• Gibbons , D. G. A. ( 1981 ). Simulation study of some ridge estimators . J. Amer. Statist. Assoc. 76 : 131 – 139 .
   Web of Science ®Google Scholar
• Hald , A. ( 1952 ). Statistical Theory with Engineering Applications . New York : Wiley .
   Google Scholar
• Hoerl , A. E. , Kennard , R. W. ( 1970a ). Ridge regression: Biased estimation for non-orthogonal problem. Technometrics 12:55–67 .
   Google Scholar
• Hoerl , A. E. , Kennard , R. W. ( 1970b ). Ridge regression: Application for non-orthogonal problem. Technometrics 12:69–82 .
   Google Scholar
• Hoerl , A. E. , Kennard , R. W. ( 1981 ). Ridge regression – 1980: Advances, algorithms, and applications . Amer. J. Mathemat. Manage. Sci. 1 : 5 – 83 .
   Google Scholar
• Kaçiranlar , S. , Sakallioğlu , S. , Akdeniz , F. , Styan , G. P. H. , Werner , H. J. ( 1999 ). A new biased estimator in linear regression and detailed analysis of the widely-analysed dataset on Portland Cement . Sankhya B 61 : 443 – 459 .
   Google Scholar
• Kaçiranlar , S. , Sakallioğlu , S. ( 2001 ). Combining the Liu estimator and the principal component regression estimator. Commun. Statist. Theor. Meth. 30(12):2699–2705 .
   Google Scholar
• Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameters for regression problems . Commun. Statist. Theor. Meth. 34 : 1177 – 1182 .
   Web of Science ®Google Scholar
• Kibria , B. M. G. ( 2003 ). Performance of some new ridge regression estimators . Commun. Statist. Simul. Computat. 32 : 419 – 435 .
   Web of Science ®Google Scholar
• Liu , K. ( 1993 ). A new class of biased estimate in linear regression . Commun. Statist. Theor. Meth. 22 : 393 – 402 .
   Web of Science ®Google Scholar
• Liu , K. ( 2003 ). Using Liu-type estimator to combat collinearity . Commun. Statist. Theor. Meth. 32 ( 5 ): 1009 – 1020 .
   Web of Science ®Google Scholar
• Mansson , K. , Shukur , G. , Kibria , B. M. G. ( 2010 ). A simulation study of some ridge regression estimators under different distributional assumptions . Commun. Statist. Simul. Computat. 39 ( 8 ): 1639 – 1670 .
   Web of Science ®Google Scholar
• Marqaards , D. W. ( 1980 ). You should standardize the predictor variables in your regression models . J. Amer. Statist. Assoc. 75 : 87 – 91 .
   Google Scholar
• McDonald , G. C. , Galarneau , D. I. A. (1975). Monte carlo evaluation of some Ridge-type estimators. J. Amer. Statist. Assoc. 70:407–416.
   Web of Science ®Google Scholar
• Muniz , G. , Kibria , B. M. G. ( 2009 ). On some ridge regression estimators: An Empirical Comparisons . Commun. Statist. Simul. Computat. 38 ( 3 ): 621 – 630 .
   Web of Science ®Google Scholar
• Nomura , M. ( 1988 ). On the almost unbiased ridge regression estimator . Commun. Statist. Simul. Computat. 17 : 729 – 743 .
   Web of Science ®Google Scholar
• Sakallioglu , S. , Kaciranlar , S. ( 2008 ). A new biased estimator based on ridge estimation . Statist. Pap. 49 : 669 – 689 .
   Web of Science ®Google Scholar
• Saleh , A. K. Md. , Kibria , B. M. G. ( 1993 ). Performances of some new preliminary test ridge regression estimators and their properties . Commun. Statist. Theor. Meth. 22 : 2747 – 2764 .
   Web of Science ®Google Scholar
• Stein , C. ( 1956 ). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proc. Third Berkeley Sympo. Math. Statist. Probab. Universiy of California, Berkeley, pp. 197–206 .
   Google Scholar
• Wood , H. , Stenior , H. H. , Starke , H. R. ( 1932 ). Effect of composition of Portland cement on heat evolved during hardening . Industr. Eng. Chem. 24 : 1207 – 1214 .
   Google Scholar