A New Strategy of Handling General Insurance Modelling Using Applied Linear Method
Abstract
This paper proposes the use of bootstrap, robust and fuzzy multiple linear regressions method in handling general insurance in order to get improved results. The main objective of bootstrapping is to estimate the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data under conditions that hold in a wide variety of econometric applications. In addition, bootstrap also provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that produce accurate results. In this paper, we emphasize the combining and modelling using bootstrapping, robust and fuzzy regression methodology. The results show that alternative methods produce better results than multiple linear regressions (MLR) model.
Keywords: Multiple linear regression; MM estimation; robust regression; bootstrap method; fuzzy regression
References
Christmann, A. (1994). Least median of weighted squares in logistic regression with large strata. Biometrika, 81, 413-417.
Donoho, D. L., & Huber, P. J. (1983). The notion of breakdown point. In Bickel P. J., Doksum K. A., & Hodges, J. L. (Eds.), A festschrift for Erich, L. Lehmann (pp. 157-184). Belmont: Wadsworth.
Draper, N., & Smith, H. (1998). Applied regression analysis (3rd ed.). New York: Wiley.
Efron B., & Tibshyrani, R.J. (1993). An introduction to the bootstrap. New-York: Chapman and Hall.
Hall, P. (1992). The bootstrap and edgeworth expansion. New-York: Springer Verlag.
Kacprzyk, J., & Fedrizzi, M. (1992). Fuzzy regression analysis. Warsaw: Omnitech Press.
Marona, R., Martin, R., & Yohai, V. J. (2006). Robust statistics theory and methods. England: John Wiley & Sons Ltd.
Nawi, M. A. A., Ahmad, W. M. A. W., & Aleng, N. A. (2012). Efficiency of general insurance in Malaysia using stochastic frontier analysis (SFA). International Journal of Modern Engineering Research, 2(5), 3886-3890.
Rousseeuw, P. J., & Leroy, A. M. (1987). Robust regression and outlier detection. New York: Wiley-Interscience.
Stromberg, A. J. (1993). Computation of high breakdown nonliner regression parameters. Journal of the American Statistical Association, 88(421), 237-244.
Yaffee, R. A. (2002). Robust Regression Analysis: Some Popular Statistical Package Options. ITS Statistics, Social Science and Mapping Group, 23, 1-12.
Yohai, V.J. (1987). High breakdown-point and high efficiency robust estimates for regression. The Annals of Statistics, 15, 642-656.
