Khurana, Mansi and Chaubey, Yogendra P. and Chandra, Shalini (2012) Jackknifing the Ridge Regression Estimator: A Revisit. Technical Report. Concordia University. (Unpublished)
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Abstract
Singh et al. (1986) proposed an almost unbiased ridge estimator using Jackknife
method that required transformation of the regression parameters. This article shows
that the same method can be used to derive the Jackknifed ridge estimator of the
original (untransformed) parameter without transformation. This method also leads in
deriving easily the second order Jackknifed ridge that may reduce the bias further. We
further investigate the performance of these estimators along with a recent method by
Batah et al. (2008) called modified Jackknifed ridge theoretically as well as numerically.
| Divisions: | Concordia University > Faculty of Arts and Science > Biology |
|---|---|
| Item Type: | Monograph (Technical Report) |
| Authors: | Khurana, Mansi and Chaubey, Yogendra P. and Chandra, Shalini |
| Series Name: | Technical Report, Mathematics and Statistics |
| Date: | February 2012 |
| Keywords: | Multicollinearity, Ridge regression, Jackknife technique |
| ID Code: | 974163 |
| Deposited By: | YOGENDRA CHAUBEY |
| Deposited On: | 20 Jun 2012 09:39 |
| Last Modified: | 20 Jun 2012 09:39 |
| References: | [1] Batah, F.S.M., Ramanathan, T.V. and Gore, S.D. (2008). The efciency of modifed
Jack-knife and ridge type regression estimators: A comparison. Surveys in Mathematics and its Applications, 3 111-122. [2] Crouse, R.H., Jin, C. and Hanumara, R.C. (1995). Unbiased ridge estimation with prior information and ridge trace. Communications in Statistics{Theory and Methods, 24(9) 2341-2354. [3] Farrar, D.E. and Glauber, R.R. (1967). Multicollinearity in regression analysis: The problem revisited. The Review of Economics and Statistics, 49(1) 92-107. [4] Farebrother, R.W. (1976). Further results on the mean square error of ridge regression. Journal of Royal Statistical Society, B38 248-250. [5] Firinguetti, L. (1989). A simulation study of ridge regression estimators with auto- correlated errors. Communications in Statistics{Simulation and Computation, 18(2) 673-702. [6] Gruber, M.H.J. (1991). The efficiency of Jack-knife and usual ridge type estimators: A comparison. Statistics and Probability Letters, 11 49-51. [7] Gruber, M.H.J. (1998). Improving Efficiency by Shrinkage: The James-Stein and Ridge Regression Estimators. New York: Marcell Dekker. [8] Hinkley, D.V. (1977). Jack-knifing in unbalanced situations. Technometrics, 19(3) 285- 292. [9] Hoerl, A.E. and Kennard, R.W. (1970). Ridge regression: Biased estimation for non- orthogonal problems. Technometrics, 20 69-82. [10] Hoerl, A.E., Kennard, R.W. and Baldwin, K. (1975). Ridge regression: Some simula- tions. Communications in Statistics{Theory and Methods, 4 105-123. [11] McDonald, G.C. and Galarneau, D.I. (1975). A Monte-Carlo evaluation of some Ridge- type estimators. Journal of the American Statistical Association, 70 407-416. [12] Miller, R.G. (1974a). The Jack-knife: A Review. Biometrika, 61 1-15. [13] Miller, R.G. (1974b). An unbalanced Jack-knife. Annals of Statistics, 2 880-891. [14] Nomura, M. (1988). On the almost unbiased ridge regression estimator. Communications in Statistics{Simulation and Computation, 17 729-743. |
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