Abstract
The goal of the credibility theory is to estimate the future claim of a given risk. The most accurate estimator is the predictive mean. If the conditional mean of losses given the risk parameter and the prior distribution of the risk parameter are known, true predictive mean can be easily obtained. However, risk parameter cannot be observed practically and it can be difficult to estimate its distribution. In this study, the structure function is estimated by using kernel density estimation with several bandwidth selection methods. For comparing the efficiences of these methods, a simulation study performed by using the data from a mixture of a lognormal conditional over a lognormal prior. The results shows that the adaptive bandwidth selection method performs better evidently for low claim severities.
Key Words:Kernel density, Adaptive bandwidth, Loss distribution, Bayesian estimation
References
- Young, V.R., Credibility using semiparametric models, ASTIN Bulletin, 27: 273-285 (1997).
- Young, V.R., Credibility using semiparametric models and a loss function with a constancy penalty, Insurance: Mathematics & Economics, 26: 151-156 (2000).
- Huang, X., Song, L., Liang, Y., Semiparametric credibility ratemaking using a piecewise linear prior, Insurance: Mathematics & Economics, 33: 585-593 (2003). Hardle, [4] implementations in S., Springer-Verlag, New York (1990). techniques with
- Silverman, B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York (1986).
- Breiman, L., Meisel, W., Purcell, E., Variable kernel estimates of multivariate densities, Technometrics, 19: 135-144 (1977).
- Abramson, I., On bandwidth variation in kernel estimates-a square root law, Annals of Statistics, 10: 1217-1223 (1982)
- Terrell, G.R. and Scott, D.W.,. Variable kernel density estimation, Annals of Statistics, 20:1236- 1265 (1992).
- Sain, S.R.,. Adaptive kernel density estimation. Ph.D. Thesis, Department of Statistics, Rice University, Houston, Texas (1994).
- Bühlmann, H.,. Experience rating and credibility, ASTIN Bulletin, 4: 199-207 (1967).
Abstract
References
- Young, V.R., Credibility using semiparametric models, ASTIN Bulletin, 27: 273-285 (1997).
- Young, V.R., Credibility using semiparametric models and a loss function with a constancy penalty, Insurance: Mathematics & Economics, 26: 151-156 (2000).
- Huang, X., Song, L., Liang, Y., Semiparametric credibility ratemaking using a piecewise linear prior, Insurance: Mathematics & Economics, 33: 585-593 (2003). Hardle, [4] implementations in S., Springer-Verlag, New York (1990). techniques with
- Silverman, B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York (1986).
- Breiman, L., Meisel, W., Purcell, E., Variable kernel estimates of multivariate densities, Technometrics, 19: 135-144 (1977).
- Abramson, I., On bandwidth variation in kernel estimates-a square root law, Annals of Statistics, 10: 1217-1223 (1982)
- Terrell, G.R. and Scott, D.W.,. Variable kernel density estimation, Annals of Statistics, 20:1236- 1265 (1992).
- Sain, S.R.,. Adaptive kernel density estimation. Ph.D. Thesis, Department of Statistics, Rice University, Houston, Texas (1994).
- Bühlmann, H.,. Experience rating and credibility, ASTIN Bulletin, 4: 199-207 (1967).
Details
| Primary Language | English |
|---|---|
| Journal Section | Statistics |
| Authors | |
| Publication Date | March 31, 2013 |
| Published in Issue | Year 2013 Volume: 26 Issue: 1 |