Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Application of Constrained Bayes Estimation under Balanced Loss Function in Insurance Pricing

  • Received : 2014.02.28
  • Accepted : 2014.04.11
  • Published : 2014.05.31
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Abstract

Constrained Bayesian estimates overcome the over shrinkness toward the mean which usual Bayes and empirical Bayes estimates produce by matching first and second empirical moments; subsequently, a constrained Bayes estimate is recommended to use in case the research objective is to produce a histogram of the estimates considering the location and dispersion. The well-known squared error loss function exclusively emphasizes the precision of estimation and may lead to biased estimators. Thus, the balanced loss function is suggested to reflect both goodness of fit and precision of estimation. In insurance pricing, the accurate location estimates of risk and also dispersion estimates of each risk group should be considered under proper loss function. In this paper, by applying these two ideas, the benefit of the constrained Bayes estimates and balanced loss function will be discussed; in addition, application effectiveness will be proved through an analysis of real insurance accident data.

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References

  1. Buhlmann, H. (1967). Experience rating and credibility I, JASTIN Bulletin, 4, 199-207.
  2. Buhlmann, H. (1969). Experience rating and credibility II, ASTIN Bulletin, 5, 157-165.
  3. Ghosh, M. (1992). Constrained Bayes estimation with applications, Journal of the American Statistical Association, 87, 533-540. https://doi.org/10.1080/01621459.1992.10475236
  4. Ghosh, M. and Kim, D. (2002). Multivariate constrained Bayes estimation, Pakistan Journal of Statis-tics, 18, 143-148.
  5. Ghosh, M., Kim, M. and Kim, D. (2007). Constrained Bayes and empirical Bayes estimation with balanced loss function, Communications in Statistics-Theory and Methods, 36, 1527-1542. https://doi.org/10.1080/03610920601125938
  6. Ghosh, M., Kim, M. and Kim, D. (2008). Constrained Bayes and empirical Bayes estimation un-der random effects normal ANOVA model with balanced loss function, Journal of Statistical Planning and Inference, 138, 2017-2028. https://doi.org/10.1016/j.jspi.2007.08.004
  7. Kim, Y., Kim, M. H. and Kim, M. J. (2012). Estimating the automobile insurance premium based on credibilities, The Korean Journal of Applied Statistics, 14, 1-14.
  8. Kim, Y. and Kim, M. (2013a). Suggestions of partial credibilities for non-life insurance premium, The Korean Journal of Applied Statistics, 26, 321-333. https://doi.org/10.5351/KJAS.2013.26.2.321
  9. Kim, M. and Kim, Y. (2013b). Constrained Bayes and empirical Bayes estimator application in insurance pricing, Communications for Statistical Applications and Methods, 20, 321-327. https://doi.org/10.5351/CSAM.2013.20.4.321
  10. Louis, T. A. (1984). Estimating a population of parameter values using Bayes and empirical Bayes method, Journal of the American Statistical Association, 79, 393-398. https://doi.org/10.1080/01621459.1984.10478062
  11. Louis, T. A. (2001). Bayes/EB Ranking, Histogram and Parameter Estimation: Issues and Research Agenda, Springer-Verlag, New York.
  12. Zellner A. (1988). Bayesian analysis in econometrics, Journal of Econometrics, 37, 27-50. https://doi.org/10.1016/0304-4076(88)90072-3
  13. Zellner, A. (1992). Bayesian and non-Bayesian estimation using balanced loss functions, Statistical Decision Theory and Related Topics V, Springer-Verlag, New York, 377-390.

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  1. A Study on the Application of Constrained Bayes Estimation for Product Quality Control vol.43, pp.1, 2015, https://doi.org/10.7469/JKSQM.2015.43.1.057
  2. Bayes Risk Comparison for Non-Life Insurance Risk Estimation vol.27, pp.6, 2014, https://doi.org/10.5351/KJAS.2014.27.6.1017