Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 50, 2016 - Issue 2
609
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

A new biased estimator in logistic regression model

&
Pages 233-253 | Received 21 Oct 2012, Accepted 16 Nov 2015, Published online: 08 Jan 2016

References

  • Myers RH, Montgomery DC, Vining GG, Robinson TJ. Generalized linear models with applications in engineering and the sciences. New Jersey: John Wiley and Sons; 2010.
  • Schaefer RL, Roi LD, Wolfe RA. A ridge logistic estimator. Comm Statist Theory Methods. 1984;13:99–113. doi: 10.1080/03610928408828664
  • Lee AH, Silvapulle MJ. Ridge estimation in logistic regression. Comm Statist Simulation Comput. 1988;17(4):1231–1257. doi: 10.1080/03610918808812723
  • Le Cessie S, Van Houwelingen JC. Ridge estimators in logistic regression. Appl Stat. 1992;41(1):191–201. doi: 10.2307/2347628
  • Mansson K, Shukur G. On ridge parameters in logistic regression. Comm Statist Theory Methods. 2011;40:3366–3381. doi: 10.1080/03610926.2010.500111
  • Schaefer RL. Alternative estimators in logistic regression when the data are collinear. J Stat Comput Simul. 1986;25:75–91. doi: 10.1080/00949658608810925
  • Smith EP, Marx BD. Ill-conditioned information matrices, generalized linear models and estimation of the effects of acid rain. Environmetrics. 1990;1(1):57–71. doi: 10.1002/env.3170010107
  • Aguilera AM, Escabias M, Valderrama MJ. Using principal components for estimating logistic regression with high-dimensional multicollinear data. Comput Statist Data Anal. 2006;50:1905–1924. doi: 10.1016/j.csda.2005.03.011
  • Hoerl AE, Kennard RW. Ridge regression: biased estimation for nonorthogonal problems. Techonometrics. 1970;12:55–67. doi: 10.1080/00401706.1970.10488634
  • Massy WF. Principal components regression in exploratory statistical research. J Amer Statist Assoc. 1965;60(309):234–256. doi: 10.1080/01621459.1965.10480787
  • Baye MR, Parker DF. Combining ridge and principal component regression:a money demand illustration. Comm Statist Theory Methods. 1984;13(2):197–205. doi: 10.1080/03610928408828675
  • Dobson AF, Barnett AG. An introduction to generalized linear models. New York: Chapmann and Hall/CRC Press; 2008.
  • Belsley DA, Kuh E, Welsch RE. Regression diagnostics: identifying influential data and sources of collinearity. New York: John Wiley; 1980.
  • Weissfeld LA, Sereika SM. A multicollinearity diagnostic for generalized linear models. Comm Statist Theory Methods. 1991;20(4):1183–1198. doi: 10.1080/03610929108830558
  • Webster JT, Gunst RF, Mason RL. Latent root regression analysis. Technometrics. 1974;16(4):513–522. doi: 10.1080/00401706.1974.10489232
  • Marx BD, Smith EP. Principal component estimation for generalized linear regression. Biometrika. 1990;77(1):23–31. doi: 10.1093/biomet/77.1.23
  • Marx BD. A continuum of principal component generalized linear regressions. Comput Statist Data Anal. 1992;13:385–393. doi: 10.1016/0167-9473(92)90113-T
  • Özkale MR. Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators. J Stat Comput Simul. 2012;82(5):653–688. doi: 10.1080/00949655.2010.550293
  • Bielza C, Robles V, Larrañaga P. Regularized logistic regression without a penalty term: an application to cancer classification with microarray data. Expert Syst Appl. 2011;38(5):5110–5118. doi: 10.1016/j.eswa.2010.09.140
  • Gill J, Generalized linear models: a unified approach, Sage University Papers Series on Quantitative Applications in the Social Sciences, Vol. 07–134. Thousand Oaks, CA: Sage; 2000.
  • Segerstedt B. On ordinary ridge regression in generalized linear models. Comm Statist Theory Methods. 1992;21(8):2227–2246. doi: 10.1080/03610929208830909
  • Vago E, Kemeny S. Logistic ridge regression for clinical data analysis (a case study). Appl Ecol Environ Res. 2006;4(2):171–179. doi: 10.15666/aeer/0402_171179
  • Farebrother RW. Further results on the mean square error of ridge regression. J R Stat Soc Ser B. 1976;38:248–250.
  • Sarkar N. Mean square error matrix comparison of some estimators in linear regressions with multicollinearity. Statist Probab Lett. 1996;30:133–138. doi: 10.1016/0167-7152(95)00211-1
  • Rao CR, Toutenburg R. Linear models: least squares and alternatives. NewYork: Springer; 1995.
  • Hoerl AE, Kennard RW, Baldwin KF. Ridge regression: some simulations. Comm Statist. 1975;4:105–123. doi: 10.1080/03610927508827232
  • Özkale MR. Principal components regression estimator and a test for the restrictions. Statistics. 2009;43(6):541–551. doi: 10.1080/02331880802605460
  • Groß J. Linear regression. New York: Springer-Verlag; 2003.
  • Lesaffre E, Marx BD. Collinearity in generalized linear regression. Commun Stat Theory Methods. 1993;22(7):1933–1952. doi: 10.1080/03610929308831126
  • Zahid FM, Ramzan S. Ordinal ridge regression with categorical predictors. J Appl Stat. 2012;161–171. doi: 10.1080/02664763.2011.578622
  • Mardia KV, Kent JT, Bibby JM. Multivariate analysis. London: Academic Press; 1979.
  • McDonald GC, Galarneau DI. A monte carlo evaluation of some ridge-type estimators. J Amer Statist Assoc. 1975;70:407–416. doi: 10.1080/01621459.1975.10479882
  • Wichern DW, Churchill GA. A comparison of ridge estimators. Technometrics. 1978;20(3):301–311. doi: 10.1080/00401706.1978.10489675
  • Newhouse JP, Oman SD. An evaluation of ridge estimators. Rand Report, No. R-716-Pr;1971:1–28.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.