Ridge Regression and James-Stein Estimation: Review and Comments

REFERENCES

• Berger , James . 1975 . Minimax estimation of location vectors over a wide class of densities . Annals of Statistics , 3 : 1318 – 1328 .
   Web of Science ®Google Scholar
• Bingham , Christopher and Larntz , Kinley . 1977 . Comment . J. Amer. Statist. Assoc. , 72 : 97 – 102 .
   Web of Science ®Google Scholar
• Bock , M. E. 1975 . Minimax estimators of the mean of a multivariate normal distribution . Annals of Statistics , 3 : 209 – 218 .
   Web of Science ®Google Scholar
• Box , George E. P. and Draper , Norman R. 1959 . A basis for the selection of a response surface design . J. Amer. Statist. Assoc. , 54 : 622 – 654 .
   Web of Science ®Google Scholar
• Box , George E. P. and Tiao , George C. 1973 . Bayesian Inference in Statistical Analysis. Reading , MA : Addison-Wesley Publishing Co. .
   Google Scholar
• Brown , Philip J. 1977 . Centering and scaling in ridge regression . Technometrics , 19 : 35 – 36 .
   Web of Science ®Google Scholar
• Brown , Philip J. and Payne , Clive . 1975 . Election night forecasting . J. Roy. Statist. Soc. , A-138 : 463 – 498 .
   Google Scholar
• Brown , William G. and Beattie , Bruce R. 1975 . Improving estimates of economic parameters by use of ridge regression with production function applications . American Journal of Agricultural Economics , 57 : 21 – 32 .
   Web of Science ®Google Scholar
• Casella , George . 1977 . Minimax ridge regression estimation Purdue University Department of Statistics Mimeograph Series #497, May
   Google Scholar
• Coniffe , D. and Stone , Joan . 1973 . A critical view of ridge regression . The Statistician , 22 : 181 – 187 .
   Google Scholar
• Coniffe , D. and Stone , Joan . 1975 . A reply to Smith and Goldstein . The Statistician , 24 : 67 – 68 .
   Google Scholar
• Dempster , A. P. 1973 . “ Alternatives to least squares in multiple regression. ” . In Multivariate Statistical Inference Edited by: Kabe , D. G. and Gupta , R. P. 25 – 40 . New York : American Elsevier Publishing Co. .
   Google Scholar
• Dempster , A. P. , Schatzoff , Martin and Wermuth , Nanny . 1977 . A simulation study of alternatives to ordinary least squares . J. Amer. Statist. Assoc. , 72 : 77 – 106 .
   Web of Science ®Google Scholar
• Draper , Norman R. and Van Nostrand , Craig R. 1978 . Ridge regression—is it worthwhile? University of Wisconsin Statistics Department Technical Report No. 501, March
   Google Scholar
• Efron , Bradley and Morris , Carl . 1972 . Limiting the risk of Bayes and empirical Bayes estimators—Part II: The empirical Bayes case . J. Amer. Statist. Assoc. , 67 : 130 – 139 .
   Web of Science ®Google Scholar
• Efron , Bradley and Morris , Carl . 1973 . Stein's estimation rule and its competitors—an empirical Bayes approach . J. Amer. Statist. Assoc. , 68 : 117 – 130 .
   Web of Science ®Google Scholar
• Efron , Bradley and Morris , Carl . 1973 . Combining possibly related estimation problems . J. Roy. Statist. Soc. , B-35 : 379 – 421 .
   Google Scholar
• Efron , Bradley and Morris , Carl . 1975 . Data analysis using Stein's estimator and its generalizations . J. Amer. Statist. Assoc. , 70 : 311 – 319 .
   Web of Science ®Google Scholar
• Efron , Bradley and Morris , Carl . 1977 . Comment . J. Amer. Statist. Assoc. , 72 : 91 – 93 .
   Web of Science ®Google Scholar
• Farebrother , R. W. 1976 . Further results on the mean square error of ridge regression . J. Roy. Statist. Soc. , B-38 : 248 – 250 .
   Google Scholar
• Gibbons , Diane Galarneau . 1978 . A simulation study of some ridge estimators. General Motors Research Laboratories Research Publication GMR-2659 (Revised) September
   Google Scholar
• Goldstein , M. and Smith , A. F. M. 1974 . Ridge-type estimators for regression analysis . J. Roy. Statist. Soc. , B-36 : 284 – 291 .
   Google Scholar
• Goldstein , M. and Smith , A. F. M. 1975 . Ridge regression: some comments on a paper of Conniffe and Stone . The Statistician , 24 : 61 – 66 .
   Google Scholar
• Golub , Gene H. , Heath , Michael and Wahba , Grace . 1979 . Generalized cross-validation as a method for choosing a good ridge parameter . Technometrics , 21 : 215 – 223 .
   Web of Science ®Google Scholar
• Gunst , Richard F. and Mason , Robert L. 1977 . Biased estimation in regression: an evaluation using mean square error . J. Amer. Statist. Assoc. , 72 : 616 – 628 .
   Web of Science ®Google Scholar
• Hemmerle , William J. 1975 . An explicit solution for generalized ridge regression . Technometrics , 17 : 309 – 314 .
   Web of Science ®Google Scholar
• Hocking , R. R. 1976 . The analysis and selection of variables in linear regression . Biometrics , 32 : 1 – 49 .
   Web of Science ®Google Scholar
• Hocking , R. R. , Speed , F. M. and Lynn , M. J. 1976 . A class of biased estimators in linear regression . Technometrics , 18 : 425 – 437 .
   Web of Science ®Google Scholar
• Hoerl , Arthur E. 1962 . Application of ridge analysis to regression problems . Chemical Engineering Progress , 60 : 54 – 59 .
   Google Scholar
• Hoerl , Arthur E. 1977 . Comment . J. Amer. Statist. Assoc. , 72 : 94 – 95 .
   Web of Science ®Google Scholar
• Hoerl , Arthur E. and Kennard , Robert W. 1970 . Ridge regression: biased estimation for nonorthogonal problems . Technometrics , 12 : 55 – 67 .
   Web of Science ®Google Scholar
• Hoerl , Arthur E. and Kennard , Robert W. 1975 . A note on a power generalization of ridge regression . Technometrics , 17 : 269
   Web of Science ®Google Scholar
• Hoerl , Arthur E. and Kennard , Robert W. 1976 . Ridge regression: iterative estimation of the biasing parameter . Comm, in Statist. , A5 : 77 – 88 .
   Google Scholar
• Hoerl , Arthur E. , Kennard , Robert W. and Baldwin , Kent F. 1975 . Ridge regression: some simulations . Comm. in Statist. , 4 : 105 – 123 .
   Google Scholar
• Hudson , H. M. 1978 . A natural identity for exponential families with applications in multiparameter estimation . Annals of Statistics , 6 : 473 – 484 .
   Web of Science ®Google Scholar
• James , W. and Stein , C. Estimation with quadratic loss . Proceedings of the Fourth Berkeley Symposium . Edited by: Neyman , Jerzy . vol. 1 , pp. 361 – 379 . Berkeley and Los Angeles : University of California Press. .
   Google Scholar
• Kendall , Maurice G. and Stuart , Alan . 1967 . The Advanced Theory of Statistics Volume 2 , New York : Hafner Publishing Co. .
   Google Scholar
• Kupper , Lawrence L. and Meydrech , Edward F. 1973 . A new approach to mean squared error estimation of response surfaces . Biometrika , 60 : 573 – 579 .
   Web of Science ®Google Scholar
• Kupper , Lawrence L. and Meydrech , Edward F. 1974 . Experimental design considerations based on a new approach to mean square error estimation of response surfaces . J. Amer. Statist. Assoc. , 69 : 461 – 463 .
   Web of Science ®Google Scholar
• Lawless , J. F. and Wang , P. 1976 . A simulation study of ridge and other regression estimators . Comm. in Statist. , A5 : 307 – 323 .
   Google Scholar
• Levenberg , Kenneth . 1944 . A method for the solution of certain non-linear problems in least squares . Quarterly of Applied Mathematics , 2 : 164 – 168 .
   Google Scholar
• Lindley , Dennis V. 1962 . Discussion . J. Roy. Statist. Soc. , B-24 : 285 – 287 .
   Google Scholar
• Lindley , D. V. and Smith , A. F. M. 1972 . Bayes estimates for the linear model . J. Roy. Statist. Soc. , B-34 : 1 – 41 .
   Google Scholar
• McDonald , Gary C. and Galarneau , Diane I. 1975 . A Monte Carlo evaluation of some ridge type estimators . J. Amer. Statist. Assoc. , 70 : 407 – 416 .
   Web of Science ®Google Scholar
• Marquardt , Donald W. 1963 . An algorithm for least-squares estimation of nonlinear parameters . SIAM , 11 : 431 – 441 .
   Google Scholar
• Marquardt , Donald W. 1970 . Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation . Technometrics , 12 : 591 – 612 .
   Web of Science ®Google Scholar
• Marquardt , Donald W. and Snee , R. D. 1975 . Ridge regression in practice . The American Statistician , 29 : 3 – 20 .
   Web of Science ®Google Scholar
• Mayer , Lawrence S. and Willke , Thomas A. 1973 . On biased estimation in linear models . Technometrics , 15 : 497 – 508 .
   Web of Science ®Google Scholar
• Newhouse , Joseph P. and Oman , Samuel D. 1971 . An evaluation of ridge estimators Rand Corporation R-716-PR
   Google Scholar
• Obenchain , R. L. 1975 . Ridge analysis following a preliminary test of the shrunken hypothesis . Technometrics , 17 : 431 – 445 .
   Web of Science ®Google Scholar
• Riley , James . 1955 . Solving systems of linear equations with a positive definite, symmetric but possibly ill-conditioned matrix . Mathematical Tables and Other Aids to Computation , 9 : 96 – 101 .
   Google Scholar
• Sclove , Stanley L. 1968 . Improved estimators for coefficients in linear regression . J. Amer. Statist. Assoc. , 63 : 596 – 606 .
   Web of Science ®Google Scholar
• Sclove , Stanley L. , Morris , Carl and Radhakrishnan , R. 1972 . Non-optimality of preliminary-test estimators for the mean of a multivariate normal distribution . Ann. Math. Statist. , 43 : 1481 – 1490 .
   Google Scholar
• Stein , Charles . Inadmissibility of the usual estimator for the mean of a multivariate normal distribution . Proceedings of the Third Berkeley Symposium . Edited by: Neyman , Jerzy . Vol. 1 , pp. 197 – 206 . Berkeley and Los Angeles : University of California Press. .
   Google Scholar
• Stein , Charles . 1960 . “ Multiple regression. ” . In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling Edited by: Olkin , Ingram . 424 – 443 . Stanford : Stanford University Press. .
   Google Scholar
• Stein , Charles . 1962 . Confidence sets for the means of a multivariate normal distribution . J. Roy. Statist. Soc. , B-24 : 265 – 296 .
   Google Scholar
• Stein , Charles . 1966 . “ An approach to the recovery of inter-block information in balanced incomplete block designs. ” . In Festschrift for J. Neyman: Research Papers in Statistics Edited by: David , F. N. 351 – 366 . New York : John Wiley and Sons. .
   Google Scholar
• Stone , M. 1973 . Discussion . J. Roy. Statist. Soc. , B-35 : 408 – 409 .
   Google Scholar
• Stone , M. 1974 . Cross-validatory choice and assessment of statistical predictions . J. Roy. Statist. Soc. , B-36 : 111 – 147 .
   Google Scholar
• Theobald , C. M. 1974 . Generalization of mean square error applied to ridge regression . J. Roy. Statist. Soc. , B-36 : 103 – 106 .
   Google Scholar
• Thiel , Henri . 1963 . On the use of incomplete prior information in regression analysis . J. Amer. Statist. Assoc. , 58 : 401 – 414 .
   Web of Science ®Google Scholar
• Thiel , Henri . 1971 . Principles of Econometrics. New York : John Wiley and Sons, Inc. .
   Google Scholar
• Thisted , Ronald A. 1976 . Ridge regression, minimax estimation, and empirical Bayes methods Stanford University Department of Biostatistics Technical Report 28, December
   Google Scholar
• Thisted , Ronald A. 1977 . Comment . J. Amer. Statist. Assoc. , 72 : 102 – 103 .
   Web of Science ®Google Scholar
• Thisted , Ronald A. 1978 . On generalized ridge regression University of Chicago Department of Statistics Technical Report 57, May
   Google Scholar
• Tukey , John W. 1957 . Approximations to the upper 5% points of Fisher's B distribution and non-central chi-square . Biometrika , 44 : 528 – 530 .
   Google Scholar
• Vinod , H. D. 1976 . Simulation and extension of a minimum mean squared error estimator in comparison with Stein's . Technometrics , 18 : 491 – 496 .
   Web of Science ®Google Scholar
• Wahba , Grace . 1976 . A survey of some smoothing problems and the method of generalized cross-validation for solving them Edited by: Krishnaiah , P. R. 507 – 523 . Amsterdam : North Holland Publishing Co. . University of Wisconsin Department of Statistics Technical Report No. 457, July. Also published (1977) in Applications of Statistics
   Google Scholar
• Wichern , Dean W. and Churchill , Gilbert A. 1978 . A comparison of ridge estimators . Technometrics , 20 : 301 – 311 .
   Web of Science ®Google Scholar
• Bibby , John and Toutenburg , Helge . 1977 . Prediction and Improved Estimation in Linear Models. New York : John Wiley and Sons. .
   Google Scholar
• Gunst , Richard F. and Mason , Robert L. 1979 . Some considerations in the evaluation of alternative prediction equations . Technometrics , 21 : 55 – 63 .
   Web of Science ®Google Scholar
• Hemmerle , W. J. and Brantle , T. F. 1978 . Explicit and constrained generalized ridge estimation . Technometrics , 20 : 109 – 120 .
   Web of Science ®Google Scholar
• Lamotte , Lynn Roy . 1978 . Bayes linear estimators . Technometrics , 20 : 281 – 290 .
   Web of Science ®Google Scholar
• Lawless , J. F. 1978 . Ridge and related estimation procedures: theory and practice . Comm. in Statist. , A7 : 139 – 164 .
   Google Scholar
• Sidik , Steven M. 1976 . Another look at biased estimation and the multicollinearity problem Unpublished MS
   Google Scholar
• Brown , P. J. 1979 . Aspects of multivariate regression . Trabajos estadistica , to appear
   Google Scholar
• Brown , P. J. and Zidek , J. V. 1979 . Adaptive multivariate ridge regression . Ann. of Statist. , 7 to appear
   Google Scholar