二阶扩散过程的非参数经验似然拟合优度检验  

The Nonparametric Empirical Likelihood Goodness-of-fit Test for Integrated Diffusion Processes

作　　者：刘再明[1] 唐明田[1,2] 王允艳[2] Liu Zaiming;Tang Mingtian;Wang Yunyan(School of Mathematics and Statistics,Central South University,Changsha 410075,China;School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]中南大学数学与统计学院,长沙410075 [2]江西理工大学理学院,赣州341000

出　　处：《数学理论与应用》2022年第3期1-20,共20页Mathematical Theory and Applications

基　　金：supported in part by the National Nature Science Foundation of China(Nos.12071487,11461032 and 11401267);the Program of Qingjiang Excellent Young Talents,Jiangxi University of Science and Technology,the Science Foundation of Jiangxi Provincial Education Department(No.GJJ190461);the Key R&D plans of Jiangxi Province(No.20202BBEL53006)。

摘　　要：本文考虑二阶扩散过程的非参数拟合优度检验问题.首先构造一个非参数检验来检验二阶扩散过程的漂移函数是否是含有未知参数的参数形式;其次,利用经验似然方法构造二阶扩散模型的拟合优度检验的检验统计量;最后,建立检验统计量的渐近分布,并通过例子验证所提出的检验方法的有效性.This paper is devoted to the nonparametric goodness-off-it test for integrated diffusion processes.Firstly,a nonparametric test is constructed for testing whether the drift function of a integrated diffusion process is of a known parametric form with unknown parameters.Secondly,a test statistic for goodness-of-fit test is obtained by applying the empirical likelihood technique.And finally,the asymptotic distribution of the test statistic is established,and then the proposed test method is applied to an example to verify its effectiveness.

关 键 词：二阶扩散过程 经验似然 拟合优度检验 Nadaraya-Watson估计量 

分 类 号：O212.1[理学—概率论与数理统计]