Length modified ridge regression

Computational Statistics and Data Analysis

Volumn 25, Issue 4, 1997, Pages 377-398

  Aldrin, Magne ^a  

^a NORWEGIAN COMPUTING CENTER   (Norway)

Author keywords

Partial least squares regression; Prediction adjusted ordinary least squares; Principal components regression; Shrunk regression; Variable subset regression

Indexed keywords

EFFICIENCY; ESTIMATION; LEAST SQUARES APPROXIMATIONS; OPTIMIZATION; VECTORS; WHITE NOISE;

RIDGE REGRESSION;

REGRESSION ANALYSIS;

ORDINARY LEAST SQUARES; REGRESSION; RIDGE REGRESSION;

EID: 0031224897     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(97)00015-7     Document Type: Article

References (22)

1. Abrahams, D., Rizzardi, F., 1988. BLSS - The Berkeley Interactive Statistical System. W.W. Norton, New York.
2. Aldrin, M., 1995. James-Stein versions of ridge regression and other biased regression methods. Technical Report STAT/5/95. Norwegian Computing Center, Oslo, submitted to Technometrics.
3. Breiman, L., Friedman, J.H., 1985. Estimating optimal transformations for multiple regression and correlation (with discussion). J. Am. Statistical Assoc. 80, 580-619.
4. Breiman, L., Spector, P., 1992. "Submodel selection and evaluation in regression. The X-random case. Internat. Statist. Rev. 60, 291-319.
5. Copas, J.B., 1983. Regression, prediction and shrinkage (with discussion). J. Roy. Statist. Soc. Ser. B 45, 311-354.
6. Fearn, T., 1983. A misuse of ridge regression in the calibration of a near infrared reflectance instrument. Appl. Statist. 32, 73-79.
7. Frank, I.E., Friedman, J.H., 1993. A statistical view of some chemometrics regression tools (with discussion). Tehnometrics 35, 109-147.
8. Gunst, R.F., Mason, R.L., 1980. Regression Analysis and it's Application. Marcel Dekker, New York.
9. Hand, D.J., Daly, F., Lunn, A.D., McConway, K.J., Ostrowski, E., 1994. A Handbook of Small Data Sets. Chapman & Hall, London.
10. Hoerl, A.E., Kennard, R.W., 1970. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 8, 27-51.
11. Hoerl, A.E., Kennard, R.W., Hoerl, R.W., 1985. Practical use of ridge regression: A challenge met, Applied Statistics 34, 114-120.
12. Hosmane, B.S., 1988. On a generalized Stein estimator of regression coefficients. Commun. Statist. Theory Methods 17, 1735-1740.
13. James, W., Stein, C., 1961. Estimation with Quadratic Loss. In: Neuman, J., (ed.), Proc. 4th Berkeley Symp. (vol. 1). University of California Press, Berkeley, pp. 361-379.
14. Mardia, K.V., Kent, J.T., Bibby, J.M., 1979. Multivariate Analysis Academic Press, London.
15. Martens, H., Næs, T., 1989. Multivariate calibration, Chichester: John Wiley & Sons.
16. Massy, W.F., 1965. Principal components regression in exploratory statistical research. J. Amer. Statist. Assoc. 60, 234-246.
17. McDonald, G.C., Schwing, R.C., 1973. Instabilities of regression estimates relating air pollution to mortality. Technometrics 15, 463-482.
18. Stone, M., Brooks, R.J., 1990. Continuum regression. Cross-validated, sequentially-constructed prediction embracing ordinary least squares, partial least squares and principal components regression (with discussion). J. Roy. Statist. Soc. Ser. B 52, 237-269.
19. Sundberg, R., 1993. Continuum regression and ridge regression. J. Roy. Statistical Soc. Ser. B 55 653-659.
20. Theil, H., 1971. Principles of Econometrics. Wiley, New York.
21. Weisberg, S., 1985. Applied Linear Regression. Wiley, New York.
22. Wold, H., 1975. Soft modeling by latent variables; the non-linear iterative partial least squares approach, in: Gani, J., (ed.), Perspectives in Probability and Statistics, Papers in Honour of M.S. Bartlett. Academic Press, London.