二阶扩散过程的非参数经验似然拟合优度检验

doi:10.3969/j.issn.1006-8074.2022.03.001

数学理论与应用 ›› 2022, Vol. 42 ›› Issue (3): 1-.doi: 10.3969/j.issn.1006-8074.2022.03.001

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二阶扩散过程的非参数经验似然拟合优度检验

刘再明¹，唐明田^1，2，*，王允艳²

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

出版日期:2022-09-30 发布日期:2022-09-28

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

Liu Zaiming¹， Tang Mingtian^1，2，*， Wang Yunyan²

1. School of Mathematics and Statistics, Central South University, Changsha 410075, China; 2. School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Online:2022-09-30 Published:2022-09-28
Contact: Tang Mingtian(1981–), PhD candidate; E-mail: mtt_csu@126.com
Supported by:
This work is 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) and the Key R & D plans of Jiangxi Province (No. 20202BBEL53006)

摘要/Abstract

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.

关键词: 二阶扩散过程, 经验似然, 拟合优度检验, Nadaraya-Watson估计量

Abstract:

This paper is devoted to the nonparametric goodness-of-fit 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.

Key words: Integrated diffusion process, Empirical likelihood, Goodness-of-fit test, Nadaraya-Watson estimator

刘再明, 唐明田, 王允艳 . 二阶扩散过程的非参数经验似然拟合优度检验[J]. 数学理论与应用, 2022, 42(3): 1-.

Liu Zaiming, Tang Mingtian, Wang Yunyan . The Nonparametric Empirical Likelihood Goodness-of-fit Test for Integrated Diffusion Processes[J]. Mathematical Theory and Applications, 2022, 42(3): 1-.

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

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