基于核估计下概率密度函数的信度模型  

Credibility models of probability density function based on kernel estimator

作　　者：章溢[1,2] 熊佳 温利民 吴贤毅[3] 周宪[4] ZHANG Yi;XIONG Jia;WEN Li-min;WU Xian-yi;ZHOU Xian(Department of Statistics,Jiangxi Normal University,Jiangxi,330022,China;School of Statistics,Jiangxi University of Finance and Economics,Jiangxi,330013,China;Department of Statistics and Actuarial Science,East China Normal University,Shanghai,200062,China;Department of Applied Finance and Actuarial Studies,Macquarie University,Sydney 2109,Australia)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022 [2]江西财经大学统计学院,江西南昌330013 [3]华东师范大学统计学院,上海200062 [4]麦考瑞大学统计与精算学系,澳大利亚悉尼2109

出　　处：《高校应用数学学报（A辑）》2020年第1期29-39,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(71761019;71771089);国家社会科学基金重大项目(19ZDA111);江西省研究生创新基金(YC2018-B059)。

摘　　要：结合核估计和信度理论的思想,建立了密度函数的Bayes模型,将条件密度函数的估计限定在核函数的线性组合中,通过最小化期望积分平方损失函数,得到了密度函数的信度估计,并研究了估计的统计性质,讨论了窗宽的最优选择方法;进而基于密度函数的信度估计,得到了各种保费原理中风险保费的信度估计,并与传统的信度估计进行了比较.Combining the idea of kernel density estimation and credibility theory,a Bayesian model of density function is established.The estimation of the conditional density function is limited to the linear combination of kernel functions.By minimizing the expected integral squared loss function,the credibility estimators of density function are obtained.In addition,the statistical properties of estimators are discussed,and the optimal selection method of window width is derived.Furthermore,based on the credibility estimation of density function,the credibility estimators of risk premiums in various premium principles are obtained.Finally,the credibility estimators of risk premiums are compared with some classical credibility formula.

关 键 词：信度理论 密度函数 核估计 保费原理 

分 类 号：O211.9[理学—概率论与数理统计]