Acta Mathematicae Applicatae Sinica

, Volume 21, Issue 2, pp 193–208

On a Strategy to Develop Robust and Simple Tariffs from Motor Vehicle Insurance Data

Original Papers

Abstract

The goals of this paper are twofold: we describe common features in data sets from motor vehicle insurance companies and we investigate a general strategy which exploits the knowledge of such features. The results of the strategy are a basis to develop insurance tariffs. We use a nonparametric approach based on a combination of kernel logistic regression and ε-support vector regression which both have good robustness properties. The strategy is applied to a data set from motor vehicle insurance companies.

Keywords

Data mining kernel logistic regression robustness statistical machine learning support vector regression 

2000 MR Subject Classification

62G08 62G35 62G32 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartlett, P.L., Tewari, A. Sparseness vs Estimating Conditional Probabilities: Some Asymptotic Results. Preprint, University of California, Berkeley, 2004Google Scholar
  2. 2.
    Celebrián, A.C., Denuit, M., Lambert, P. Generalized Pareto Fit to the Society of Actuaries’ Large Claims Database. North American Actuarial Journal, 7: 18–36 (2003)MathSciNetGoogle Scholar
  3. 3.
    Cherkassky, V., Ma, Y. Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks, 17: 113–126 (2004)MATHCrossRefGoogle Scholar
  4. 4.
    Christmann, A., Fischer, P., Joachims, T. Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassi.cations. Computational Statistics, 17: 273–287 (2002)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Christmann, A., Rousseeuw, P.J. Measuring overlap in logistic regression. Computational Statistics and Data Analysis, 37: 65–75 (2001)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Christmann, A., Steinwart, I. On robust properties of convex risk minimization methods for pattern recognition. Journal of Machine Learning Research, 5: 1007–1034 (2004a)Google Scholar
  7. 7.
    Christmann, A., Steinwart, I. Consistency and robustness of kernel based regression. University of Dortmund, SFB-475, TR-01/05 Submitted, 2005Google Scholar
  8. 8.
    Embrechts, P., Klüppelberg, C., Mikosch, T. Modelling Extreme Events for Insurance and Finance. Springer-Verlag, Berlin, 1997Google Scholar
  9. 9.
    Hastie, T., Tibshirani, R. Classification by pairwise coupling. Annals of Statistics, 26: 451–471 (1998)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Keerthi, S.S., Duan, K., Shevade, S.K., Poo, A.N. A fast dual algorithm for kernel logistic regression. In Machine Learning: Proceedings of the Ninetheenth International Conference, Kaufmann, San Francisco, 299–306 2004Google Scholar
  11. 11.
    Leisch, F. et al. R package e1071. http://cran.r-project.org, 2003Google Scholar
  12. 12.
    Nelder, J.A., Mead, R. A simplex algorithm for function minimization. Computer Journal, 7: 308–313 (1965)Google Scholar
  13. 13.
    Rousseeuw, P.J., Christmann, A. Robustness against separation and outliers in logistic regression. Computational Statistics & Data Analysis, 43: 315–332 (2003)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Rüping, S. myKLR - kernel logistic regression. Department of Computer Science, University of Dortmund. http://www-ai.cs.uni-dortmund.de/SOFTWARE, 2003Google Scholar
  15. 15.
    Schölkopf, B., Smola, A. Learning with Kernels. Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, Massachusetts, 2002 Google Scholar
  16. 16.
    Steinwart, I. On the Influence of the Kernel on the Consistency of Support Vector Machines. Journal of Machine Learning Research, 2: 67–93 (2001)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Vapnik, V. Statistical Learning Theory. John Wiley & Sons, New York, 1998Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of DortmundDortmundGermany

Personalised recommendations