Some Criticisms of Stochastic Shrinkage and Ridge Regression, With Counterexamples

REFERENCES

• Baranchik , A. 1964 . “Multiple Regression and Estimation of the Mean of a Multivariate Normal Distribution,” Stanford University, Dept. of Statistics. . Technical Report No. 51
   Google Scholar
• Bhattacharya , P. K. 1966 . “Estimating the Mean of a Multivariate Normal Population With General Quadratic Loss Function,” . Ann. Math. Statist. , 37 : 1819 – 1824 .
   Google Scholar
• Bibby , J. and Toutenberg , H. 1977 . Prediction and Improved Estimation in Linear Models New York : John Wiley. .
   Google Scholar
• Dempster , A. P. , Schatzoff , M. and Wermuth , N. 1977 . “A Simulation Study of Alternatives to Ordinary Least Squares,” . J. Amer. Statist. Assoc. , 72 : 77 – 106 .
   Web of Science ®Google Scholar
• Draper , N. R. and Van Nostrand , R. C. 1980 . “Ridge Regression and James-Stein Estimation: Review and Comments,” . Technometrics , 21 : 451 – 465 .
   Web of Science ®Google Scholar
• Efron , B. and Morris , C. 1976 . “Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution,” . Ann. Statist. , 4 : 11 – 21 .
   Web of Science ®Google Scholar
• Egerton , M. F. and Laycock , P. J. 1979 . “An Explicit Formula for the Risk of James-Stein Estimators,” University of Manchester Institute of Science and Technology, Dept. of Mathematics. . Technical Report No. 109
   Google Scholar
• Gibbons , D. I. 1981 . “A Simulation Study of Some Ridge Estimators,” . J. Amer. Statist. Assoc. , 76 : 131 – 139 .
   Web of Science ®Google Scholar
• Hoerl , A. E. 1962 . “Application of Ridge Analysis to Regression Problems,” . Chem. Eng. Progr. , 58 : 54 – 59 .
   Google Scholar
• Hoerl , A. E. 1964 . “Ridge Analysis,” . Chem. Eng. Progr. , 60 : 67 – 77 .
   Google Scholar
• Hoerl , A. E. and Kennard , R. W. 1970a . “Ridge Regression: Biased Estimation for Non-orthogonal Problems,” . Technometrics , 12 : 55 – 67 .
   Web of Science ®Google Scholar
• Hoerl , A. E. and Kennard , R. W. 1970b . “Ridge Regression: Applications to Non-orthogonal Problems,” . Technometrics , 12 : 69 – 82 .
   Web of Science ®Google Scholar
• James , J. F. and Stein , C. M. “Estimation With Quadratic Loss,” . Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability . pp. 361 – 379 . Berkeley : University of California Press. .
   Google Scholar
• Lawless , J. F. and Wang , P. 1976 . “A Simulation Study of Ridge and Other Regression Estimators,” . Communications in Statistics , 5 : 307 – 323 .
   Google Scholar
• Mayer , L. S. and Willke , T. A. 1973 . “On Biased Estimation in Linear Models,” . Technometrics , 15 : 497 – 508 .
   Web of Science ®Google Scholar
• Mcdonald , G. C. and Calarneau , D. I. 1975 . “A Monte Carlo Evaluation of Some Ridge-Type Estimators,” . J. Amer. Statist. Assoc. , 70 : 407 – 416 .
   Web of Science ®Google Scholar
• Obenchain , R. L. 1975 . “Ridge Analysis Following a Preliminary Test of the Shrunken Hypothesis,” . Technometrics , 17 : 431 – 442 .
   Web of Science ®Google Scholar
• Obenchain , R. L. 1978 . “Good and Optimal Ridge Estimators,” . Ann. Statist. , 6 : 1111 – 1121 .
   Web of Science ®Google Scholar
• Smith , G. and Campbell , F. 1980 . A Critique of Some Ridge Regression Methods,” . J. Amer. Statist. Assoc. , 75 : 74 – 103 .
   Web of Science ®Google Scholar
• Stein , C. M. “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution,” . Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability . pp. 197 – 206 . Berkeley : University of California Press. .
   Google Scholar
• Strawderman , W. E. 1978 . “Minimax Adaptive Generalized Ridge Regression Estimators,” . J. Amer. Statist. Assoc. , 73 : 623 – 627 .
   Web of Science ®Google Scholar
• Theobald , C. M. 1974 . “Generalisations of Mean Square Error Applied to Ridge Regression,” . J. Roy. Statist. Soc. , 36 : 103 – 106 . Ser. B
   Google Scholar
• Whittle , P. and Stein , C. M. 1962 . J. Roy. Statist. Soc. , 24 : 285 – 296 . Discussion of a paper by, Ser. B
   Google Scholar