Some Liu and ridge-type estimators and their properties under the ill-conditioned Gaussian linear regression model

References

• Judge , G. G. and Bock , M. E. 1978 . The Statistical Implications of Pre-test and Stein-rule Estimators in Econometrics , Amsterdam : North-Holland Publishing Company .
   Google Scholar
• Saleh , A. K.Md.E. 2006 . Theory of Preliminary Test and Stein-type Estimation with Applications , New York : John Wiley .
   Google Scholar
• Bancroft , T. A. 1944 . On biases in estimation due to use of preliminary tests of significance . Ann. Math. Stat. , 15 : 190 – 204 .
   Google Scholar
• Bancroft , T. A. 1964 . Analysis and inference for incompletely specified models involving the use of preliminary test(s) of significance . Biometrics , 20 : 427 – 442 .
   Web of Science ®Google Scholar
• Han , C.-P. and Bancroft , T. A. 1968 . On pooling means when variance is unknown . J. Am. Statist. Assoc. , 63 : 1333 – 1342 .
   Web of Science ®Google Scholar
• Saleh , A. K.Md.E. and Sen , P. K. 1978 . Non-parametric estimation of location parametric after a preliminary test regression . Ann. Stat. , 6 : 154 – 168 .
   Web of Science ®Google Scholar
• Ahmed , S. E. and Saleh , A. K.M.E. 1990 . Estimation strategies for the intercept vector in a simple linear multivariate regression model . J. Comput. Statist. Data Anal. , 10 : 193 – 206 .
   Web of Science ®Google Scholar
• Giles , A. J. 1991 . Pretesting for linear restrictions in a regression model with spherically symmetric distributions . J. Econom. , 50 : 377 – 398 .
   Web of Science ®Google Scholar
• Benda , N. 1996 . Pre-test estimation and design in the linear model . J. Statist. Plann. Inference , 52 : 225 – 240 .
   Web of Science ®Google Scholar
• Ahmed , S. E. , Volodin , A. I. and Volodin , I. N. 2009 . High order approximation for the coverage probability by confident set cantered at the positive-part James–Stein estimator . Stat. Probab. Lett. , 79 : 1823 – 1828 .
   Web of Science ®Google Scholar
• Saleh , A. K.Md.E. , Tang , F. and Kibria , B. M.G. 2009 . Improved estimation of the parameters of simple linear regression model with autocorrelated errors . J. Statist. Res. , 43 : 89 – 107 .
   Google Scholar
• Hoerl , A. E. and Kennard , R. W. 1970 . Liu: Biased estimation for non-orthogonal problems . Technometrics , 12 : 55 – 67 .
   Web of Science ®Google Scholar
• Malthouse , E. C. 1999 . Shrinkage estimation and direct marketing scoring model . J. Interact. Mark. , 13 ( 4 ) : 10 – 23 .
   Google Scholar
• Gibbons , D. G.A. 1981 . Simulation study of some ridge estimators . J. Am. Statist. Assoc. , 76 : 131 – 139 .
   Web of Science ®Google Scholar
• Sarker , N. 1992 . A new estimator combining the ridge regression and the restricted least squares method of estimation . Commun. Statist. A , 21 ( 7 ) : 1987 – 2000 .
   Google Scholar
• Saleh , A. K.Md. and Kibria , B. M.G. 1993 . Performances of some new preliminary test ridge regression estimators and their properties . Commun. Stat. Theory Methods , 22 : 2747 – 2764 .
   Web of Science ®Google Scholar
• Gruber , M. H.J. 1998 . Improving efficiency by shrinkage the James–Stein and Liu estimators , New York : Springer Verlag .
   Google Scholar
• Singh , S. and Tracy , D. S. 1999 . Ridge-regression using scrambled responses . Metron , LVII : 147 – 157 .
   Google Scholar
• Wencheko , E. 2000 . Estimation of the signal-to-noise in the linear regression model . Statist. Papers , 41 : 327 – 343 .
   Web of Science ®Google Scholar
• Inoue , T. 2001 . Improving the ‘HKB’ ordinary type ridge estimators . J. Jpn Statist. Soc. , 31 ( 1 ) : 67 – 83 .
   Google Scholar
• Kibria , B. M.G. 2003 . Performance of some new ridge regression estimators . Commun. Stat. Simul. Comput. , 32 : 419 – 435 .
   Web of Science ®Google Scholar
• Kibria , B. M.G. 2004 . Performance of the shrinkage preliminary test ridge regression estimators based on the conflicting of W, LR and LM tests . J. Statist. Comput. Simul. , 74 ( 11 ) : 793 – 810 .
   Web of Science ®Google Scholar
• Kibria , B. M.G. 2006 . Applications of some improved estimators in linear regression . J. Mod. Appl. Statist. Methods , 5 ( 2 ) : 367 – 380 .
   Google Scholar
• Muniz , G. and Kibria , B. M.G. 2009 . On some ridge regression estimators: An empirical comparisons . Commun. Stat. Simul. Comput. , 38 ( 3 ) : 621 – 630 .
   Web of Science ®Google Scholar
• Liu , K. 1993 . A new class of biased estimate in linear regression . Commun. Stat. Theory Methods , 22 : 393 – 402 .
   Web of Science ®Google Scholar
• Stein , C. Inadmissibility of the usual estimator of the mean of a multivariate normal distribution . Proceedings of the 3rd Berkely Symposium on Mathematical Statistics and Probability . Vol. 1 , pp. 97 – 206 .
   Google Scholar
• Kaciranlar , S. , Sakallioglu , S. , Akdeniz , F. , Styan , G. P.H. and Werner , H. J. 1999 . A new biased estimator in linear regression and a detailed analysis of the widely-analyzed dataset on Portland cement . Sankhya , B-61 : 443 – 459 .
   Google Scholar
• Yuksel , F. and Akdeniz , F. 2001 . Properties of some new preliminary test Liu estimators and comparisons with the usual preliminary test estimators . J. Statist. Res. , 35 : 45 – 56 .
   Google Scholar
• Alheety , M. I. , Gore , S. D. and Kibria , B. M.G. 2008 . A new biased estimator for the restricted linear regression model . J. Statist. Theory Appl. , 7 ( 3 ) : 293 – 302 .
   Google Scholar
• Yang , H. and Xu , J. 2011 . Preliminary test Liu estimators based on the conflicting W, LR and LM tests in a regression model with multivariate t error . Metrika , 73 ( 3 ) : 275 – 292 .
   Web of Science ®Google Scholar
• Anderson , T. W. 2003 . An Introduction to Multivariate Statistical Analysis , 3 , New York : John Wiley .
   Google Scholar