Assessing Influence on the Liu Estimates in Linear Regression Models

References

• Banerjee , M. , Frees , E. W. ( 1997 ). Influence diagnostics for linear longitudinal models . J. Amer. Statist. Assoc. 92 : 999 – 1005 .
   Web of Science ®Google Scholar
• Beckman , R. J. , Nachtsheim , C. J. , Cook , R. D. ( 1987 ). Diagnostics for mixed-model analysis of variance . Technometrics 29 : 413 – 26 .
   Web of Science ®Google Scholar
• Belsley , D. A. , Kuh , E. , Welsch , R. E. ( 1980 ). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity . New York : John Wiley & Sons .
   Google Scholar
• Belsley , D. A. ( 1991 ). Conditioning Diagnostics: Collinearity and Weak Data in Regression . New York : John Wiley & Sons .
   Google Scholar
• Billor , N. ( 1992 ). Diagnostics methods in ridge regression and errors-in-variables model. Ph.D. Thesis. University of Sheffield, UK .
   Google Scholar
• Billor , N. , Loynes , R. M. ( 1999 ). An application of the local Influence approach to ridge regression . J. Appl. Statist. 26 : 177 – 183 .
   Web of Science ®Google Scholar
• Chatterjee , S. , Hadi , A. S. ( 1986 ). Influential observations, high leverage points, and outliers in linear regression . Statist. Sci. 1 : 379 – 393 .
   Google Scholar
• Chatterjee , S. , Hadi , A. S. ( 1988 ). Sensitivity Analysis in Linear Regression . New York : John Wiley & Sons .
   Google Scholar
• Christensen , R. , Pearson , L. M. , Johnson , W. ( 1992 ). Case-deletion diagnostics for mixed models . Technometrics 34 : 38 – 45 .
   Web of Science ®Google Scholar
• Cook , R. D. ( 1977 ). Detection of influential observation in linear regression . Technometrics 19 : 15 – 18 .
   Web of Science ®Google Scholar
• Cook , R. D. ( 1986 ). Assessment of local influence . J. Roy. Statist. Soc. Ser. (B) 48 : 133 – 169 .
   Web of Science ®Google Scholar
• Cook , R. D. , Weisberg , S. ( 1982 ). Residuals and Influence in Regression . New York : Chapman and Hall .
   Google Scholar
• Draper , N. R. , John , J. A. ( 1981 ). Influential observations and outliers in regression . Technometrics 23 : 21 – 26 .
   Web of Science ®Google Scholar
• Farrar , D. E. , Galuber , R. R. ( 1967 ). Multicollinearity in regression analysis: the problem-revisited . Rev. Econ. Statist. 49 : 92 – 107 .
   Web of Science ®Google Scholar
• Feldstein , M. S. ( 1973 ). Multicollinearity and the mean squared error of alternative estimators . Econometrica 41 : 337 – 346 .
   Web of Science ®Google Scholar
• Foong , N. S. , Chin , L. H. , Hoe , Q. S. ( 2007 ). An overview of biased estimators . J. Phys. Sci. 18 : 89 – 106 .
   Google Scholar
• Haitovsky , Y. ( 1969 ). Multicollinearity in regression analysis: comment . Rev. Econ. Statist. 51 : 486 – 489 .
   Web of Science ®Google Scholar
• Hoaglin , D. C. , Welsch , R. E. ( 1978 ). The Hat matrix in regression and ANOVA . Amer. Statistician 32 : 17 – 22 .
   Web of Science ®Google Scholar
• Hoerl , A. E. , Kennard , R. W. ( 1970 ). Ridge regression: biased estimation for non-orthogonal problems . Technometrics 12 : 55 – 67 .
   Web of Science ®Google Scholar
• Hubert , M. H. , Wijekoon , P. ( 2006 ). Improvement of the Liu estimator in linear regression model . Statist. Pap. 47 : 471 – 479 .
   Web of Science ®Google Scholar
• Jahufer , A. , Jianbao , C. ( 2009 ). Assessing global influential observations in modified ridge regression . Statist. Probab. Lett. 79 : 513 – 518 .
   Web of Science ®Google Scholar
• Jahufer , A. , Jianbao , C. ( 2011 ). Measuring local influential observations in modified ridge regression . J. Data Sci. 9 : 359 – 372 .
   Google Scholar
• Kaciranlar , S. , Sakallioğlu , S. ( 2001 ). Combining the Liu estimator and the principal component regression estimator . Commun. Statist. Theor. Meth. 30 : 2699 – 2705 .
   Web of Science ®Google Scholar
• Kaciranlar , S. , Sakallioğlu , S. , Akdeniz , F. , Styan , G. P. H. , Werner , H. J. (1999). A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland cement. Sankhya Ind. J. Statist. 61:443–459.
   Google Scholar
• Kim , C. , Lee , Y. , Park , B. U. ( 2001 ). Cook's distance in local polynomial regression . Statist. Probab. Lett. 54 : 33 – 40 .
   Web of Science ®Google Scholar
• Klein , L. R. ( 1962 ). An Introduction to Econometrics . Englewood Eliffs , NJ : Prentice Hall, Inc .
   Google Scholar
• Lee , S. Y. , Lu , B. , Song , X. Y. ( 2006 ). Assessing local influence for nonlinear structural equation models with ignorable missing data . Computat. Statist. & Data Anal. 50 : 1356 – 1377 .
   Web of Science ®Google Scholar
• Leiva , V. , Barros , M. , Paula , G. A. , Galea , M. ( 2007 ). Influence diagnostics in log-Birnbaum-Saunders regression models with censored data . Computat. Statist. Data Anal. 51 : 5694 – 5707 .
   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
• Longley , J. W. ( 1967 ). An appraisal of least squares programs for the electronic computer from the point of view of the user . J. Amer. Statist. Assoc. 62 : 819 – 841 .
   Web of Science ®Google Scholar
• Mallows , C. L. ( 1973 ). Some comments on c p . Technometrics 15 : 661 – 675 .
   Web of Science ®Google Scholar
• Mandel , J. ( 1982 ). Use of the singular value decomposition in regression analysis . Amer. Statistician 36 : 15 – 24 .
   Web of Science ®Google Scholar
• Marquardt , D. W. ( 1970 ). Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation . Technometrics 12 : 591 – 612 .
   Web of Science ®Google Scholar
• Martin , M. A. , Roberts , S. , Zheng , L. ( 2010 ). Delete-2 and delete-3 jackknife procedures for unmasking in regression . Austral. NZ J. Statist. 52 : 45 – 60 .
   Web of Science ®Google Scholar
• Mason , R. L. , Gunst , R. F. ( 1985 ). Outlier-induced Collinearities . Technometrics 27 : 401 – 407 .
   Web of Science ®Google Scholar
• McDonald , G. C. , Galarneau , D. I. ( 1975 ). A Monto Carlo evaluation of some ridge type-estimators . J. Amer. Statist. Assoc. 70 : 407 – 416 .
   Web of Science ®Google Scholar
• Myers , R. H. ( 1986 ). Classical and Modern Regression with Applications . Boston : Duxbury Press .
   Google Scholar
• Pena , D. ( 1991 ). Measuring influence in dynamic regression models . Technometrics 33 : 93 – 101 .
   Web of Science ®Google Scholar
• Preisser , J. S. , Qaqish , B. F. ( 1996 ). Deleting diagnostics for generalized estimating equations . Biometrika 83 : 551 – 562 .
   Web of Science ®Google Scholar
• Prendergast , L. A. ( 2006 ). Detecting influential observations in sliced inverse regression analysis . Austral. NZ. J. Statist. 48 : 285 – 304 .
   Web of Science ®Google Scholar
• Quantitative Micro Software . ( 2002 ). EViews 4 User's Guide . Irvine , CA : Quantitative Micro Software, LLC .
   Google Scholar
• Rao , C. R. ( 1973 ). Linear Statistical Inference and Its Applications . New York : John Wiley & Sons .
   Google Scholar
• Rasekh , A. R. , Fieller , N. R. J. ( 2004 ). Influence functions in functional measurement error models with replicated data . Statistics 37 : 169 – 178 .
   Web of Science ®Google Scholar
• Rasekh , A. , Mohtashami , G. ( 2007 ). Assessing influence on ridge estimates in functional measurement error models . Ann. DE L'I. S. U. P. Publ. Inst. Statist. Univ. Paris, Fascicule 1–2 , 97 – 109 .
   Google Scholar
• Roy , S. S. , Guria , S. ( 2008 ). Diagnostics in logistic regression models . J. Kor. Statist. Soc. 37 : 89 – 94 .
   Web of Science ®Google Scholar
• Sakallioglu , S. , Kaciranlar , S. , Akdeniz , F. ( 2001 ). Mean squared error comparisons of some biased regression estimators . Commun. Statist. Theor. Meth. 30 : 347 – 361 .
   Web of Science ®Google Scholar
• Sarkar , N. ( 1992 ). A new estimator combining the ridge regression and the restricted least squares methods of estimation . Commun. Statist. Theor. Meth. 21 : 1987 – 2000 .
   Web of Science ®Google Scholar
• Shi , L. , Wang , X. ( 1999 ). Local influence in ridge regression . Computat. Statist. Data Anal. 31 : 341 – 353 .
   Web of Science ®Google Scholar
• Singh , B. , Chaubey , Y. P. , Dwivedi , T. D. ( 1986 ). An almost unbiased ridge estimator . Sankhya, Series (B) 48 : 342 – 346 .
   Google Scholar
• Steece , B. M. ( 1986 ). Regression space outliers in ridge regression . Commun. Statist. Theor. Meth. 15 : 3599 – 3605 .
   Web of Science ®Google Scholar
• Stein , C. (1956). Inadmissibility of usual estimator for the mean of a multivariate normal distribution. Proc. The Third Berkeley Symp. Math. Stat. and Prob . Berkeley University of California Press, pp. 197–206.
   Google Scholar
• Swindel , B. F. ( 1976 ). Good ridge estimators based on prior information . Commun. Statist. Theor. Meth. 17 : 1065 – 1075 .
   Web of Science ®Google Scholar
• Takeuchi , H. ( 1991 ). Detecting influential observations by using a new expression of Cook's distance . Commun. Statist. Theor. Meth. 20 : 261 – 274 .
   Google Scholar
• Ullah , M. A. , Pasha , G. R. ( 2009 ). The origin and developments of influence measures in regression . Pakistan J. Statist. 25 : 295 – 307 .
   Web of Science ®Google Scholar
• Walker , E. , Birch , J. B. ( 1988 ). Influence measures in ridge regression . Technometrics 30 : 221 – 227 .
   Web of Science ®Google Scholar
• Weissfeld , L. A. , Schneider , H. ( 1990 ). Influence diagnostics for the Weibull model fit to censored data . Statist. Probab. Lett. 9 : 67 – 73 .
   Web of Science ®Google Scholar
• Xie , F. C. , Wei , B. C. ( 2009 ). Diagnostics for generalized Poisson regression models with errors in variables . J. Statist. Computat. Simul. 79 : 909 – 922 .
   Web of Science ®Google Scholar
• Zewotir , T. , Galpin , J. S. ( 2005 ). Influence diagnostics for linear mixed models . J. Data Sci. 3 : 153 – 177 .
   Google Scholar
• Zhao , Y. , Lee , A. H. ( 1998 ). Influence diagnostics for simultaneous equations models . Austral. NZ. J. Statist. 40 : 345 – 358 .
   Web of Science ®Google Scholar