Brown, L. (1975). "Estimation with incompletely specified loss functions (the case
of several location parameters.)" **Journal American Statistical Association** 70,
417-427.

Breiman, L. (1995). "Better subset regression using the non-negative
garrote." **Technometrics** 37, 373-384.

Bunke, 0. (1975). "Least squares estimators as robust and minimax
estimators." **Math. Operations forsch u. Statist.** 6, 687-688.

Burr, TL and Fry, HA. (2005).
"Biased regression: the case for cautious application." **Technometrics**
47, 284-296. **[**Includes references to material on this website.]

Casella, G. (1980). "Minimax ridge regression estimation." **Annals of
Statistics** 8, 1036-1056.

Casella, G. (1985). "Condition numbers and minimax ridge-regression
estimators." **Journal American Statistical Association** 80, 753-758.

Chatterjee, S and Hadi, A. S. (1988). **Sensitivity Analysis in Regression.** New
York: John Wiley.

Cook, R. D. and Weisberg, S. (1994). **Introduction to Regression Graphics.** New
York: John Wiley.

Cook, R. D. (1977). "Detection of influential observations in linear
regression." **Technometrics** 19, 15-18.

Croghan, T.W., Obenchain. R.L. and Crown, W.E. (1998). "What does treatment of
depression really cost?" **Health Affairs** 17(4); 198-208. **
View/Download Paper and Technical Appendix**

Efron B. and Morris, C. N. (1976). "Discussion" (of Dempster, Schatzoff and
Wermuth.) **Journal American Statistical Association** 72, 91-93.

Efron B, Hastie T, Johnstone I, Tibshirani R.
(2004)**. **“Least Angle Regression.”** Annals of Statistics **32:
407-499 (with discussion.)

Frank, I. E. and Freidman, J. H. (1993). "A statistical view of some chemometrics
regression tools." (with discussion) **Technometrics** 35, 109-148.

Fu, W. J. (1997). "Penalized Regressions: the Bridge versus the Lasso." One
of 4 winners in the 1997 student paper competition sponsored by the **ASA
Statistical Computing Section**.

Wenjiang's thesis under Rob Tibshani at the University of Toronto is entitled "A Statistical Shrinkage Model and Its Applications."

Gibbons, D. G. (1981). "A simulation study of some ridge estimators." **Journal
of the American Statistical Association** 76, 131-139.

Goldstein M. and Smith, A. F. M (1974). "Ridge-type estimators for regression
analysis." **Journal of the Royal Statistical Society B** 36, 284-291.

Golub, G. H., Heath, M., and Wahba, G. (1979). "Generalized cross- validation as a
method for choosing a good ridge parameter." **Technometrics** 21, 215-223.

Gruber, M. H. J. (1998). **Improving Efficiency by Shrinkage:** The
James-Stein and Ridge Regression Estimators. New York: Marcel Dekker.

Hoerl, A. E. and Kennard, R. W. (1970a). "Ridge regression: biased estimation for
nonorthogonal problems." **Technometrics** 12, 55-67.

Hoerl, A. E. and Kennard, R. W. (1970b). "Ridge regression: applications to
nonorthogonal problems." **Technometrics** 12, 69-82.

LeBlanc, M. and Tibshirani, R. (1998). "Monotone shrinkage of trees."
**Journal of Computational and Graphical Statistics** 7, 417-433.

Longley, J. W. (1967). "An appraisal of least squares programs for the electronic
computer from the point of view of the user." **Journal of the American Statistical
Association** 62, 819-841.

Mallows, C. L. (1973). "Some comments on Cp." **Technometrics** 15,
661-677.

Mallows, C. L. (1995). "More comments on Cp." **Technometrics** 37,
362-372.

Marquardt, D. W. (1970). "Generalized inverses, ridge regression, biased linear
estimation, and nonlinear estimation." **Technometrics** 12, 591-612.

Marquardt, D. W. (1980). "Comment: You should standardize the predictor variables
in your regression models." **Journal of the American Statistical Association**
75, 87-91.

Massy, W. F. (1965). "Principal components regression in exploratory statistical
research." **Journal American Statistical Association** 60, 234-256.

Nash, J. C. (1992). "Statistical shareware: illustrations from regression
techniques." **The American Statistician** 46, 312-318.

Nash reviewed PC software that included softRX freeware stand-alone (DOS) applications.

Obenchain, R. L. and Vinod, H. (1974). "Estimates of partial derivatives from ridge regression on ill-conditioned data." NBER-NSF Seminar on Bayesian Inference in Econometrics, Ann-Arbor, Michigan.

Obenchain, R. L. (1975a). "Residual optimality: ordinary vs. weighted vs. biased
least squares." **Journal of the American Statistical Association** 70, 375-379.

Ordinary least squares and diagonally-weighted least squares always produce residuals that are optimal estimators of lack-of-fit ...even when the expectation model and/or dispersion model you have specified are/is wrong!

Obenchain, R. L. (1975b). "Ridge analysis following a preliminary test of the
shrunken hypothesis" (with discussion.) **Technometrics** 17, 431-445.

Classical, normal-theory monitoring of the likelihood-of-MSE-optimality along ANY shrinkage path.

Obenchain, R. L. (1977). "Classical F-tests and confidence regions for ridge
regression." **Technometrics** 19, 429-439.

See this paper and/or my Frequently-Asked-Questions page for information on confidence intervals in shrinkage regression.

Obenchain, R. L. (1978). "Good and optimal ridge estimators." **Annals of
Statistics** 6, 1111-1121.

The "ridge-function" theorem; maximum likelihood estimation of the "inferior direction" and of scaled MSE risk along any direction in p-dimensional regression coefficient space; MSE risk optimality of 0 or X'y along directions orthogonal to or parallel to beta, respectively.

Obenchain, R. L. (1980). Comment on "A critique of some ridge regression
methods." **Journal of the American Statistical Association **75, 95-96.

Obenchain, R. L. (1981). "Maximum likelihood ridge regression and the shrinkage
pattern alternatives." **I.M.S. Bulletin** 10, 37; Absract 81t-23. (67 page review
article.)

Obenchain, R. L. (1984). "Maximum likelihood ridge displays." **Communications
in Statistics A** 13, 227-240.

Proceedings of the Fordham Ridge Symposium, ed. H. D. Vinod; illustrations of usage of RXridge SAS/IML freeware.

Obenchain, R. L. (1995). "Maximum likelihood ridge regression." **Stata
Technical Bulletin** 28, 22-36. View/Download Paper

Introduction to basic shrinkage/ridge concepts; illustrations of usage of RXridge .ADO freeware.

Obenchain, R. L. (1996-2005). **Shrinkage Regression: ridge, BLUP, Bayes and Stein.**
Unfinished eBook draft (185 pages.)

Obenchain, R. L. (1997). "Maximum likelihood shrinkage in regression."

Obenchain, R. L. (1998). "Influential observations in ridge regression."

Use the main eBook MENU to download PDFs for any of the above three items.

Obenchain, R. L. (2005). **RXshrink: **an R package for maximum likelihood
shrinkage in generalized (2-parameter) ridge regression or least angle
regression (LAR). * CRAN.R-project.org
*Or...

Obenchain RL. * PDF File*
containing copies of all the

Shumway, R. H. (1982). "Maximum likelihood estimation of the ridge parameter in linear regression." Technical Report, Department of Statistics, University of California at Davis.

Stein, C. M. (1956). "Inadmissibility of the usual estimator of the mean of a
multivariate normal distribution." **Proceedings of the Third Berkeley Symposium on
Mathematical Statistics and Pobability** 1, 197-206. University of California Press.

Strawderman, W. E. (1978). "Minimax adaptive generalized ridge regression
estimators." **Journal American Statistical Association** 73, 623-627.

Theil, H. (1963). "On the use of incomplete prior information in regression
analysis." **Journal of the American Statistical Association** 58, 401-414.

Thisted, R. (1976). "Ridge regression, minimax estimation, and empirical bayes methods." Technical Report No. 28, Division of Biostatistics, Stanford University.

Tibshirani, R. (1996). "Regression shrinkage and selection via the lasso." **Journal
of the Royal Statistical Society B** 58, 267-288.

Tierney, Luke. (1990). **LISP-STAT: An Object-Oriented Environment for Statistical
Computing and Dynamic Graphics.** New York: John Wiley and Sons.

Tukey, J. W. (1975). "Instead of Gauss-Markov Least Squares; What?" **Applied
Statistics,** ed. R. P. Gupta. Amsterdam-New York: North Holland Publishing Company.

Vinod, H. D. and Ullah, A. (1981). **Recent Advances in Regression Methods.**
New York: Marcel Dekker.

Vinod, H. D. (1995). "Double bootstrap for shrinkage estimators." **Journal
of Econometrics** 68, 287-302.

Walter, Bernhard (1994). "XLisp-Stat code for shrinkage/ridge regression." Techniche Universitad Munich.