Non-adaptive estimation for degenerate diffusion processes

IF 0.4 Q4 STATISTICS & PROBABILITY
A. Gloter, Nakahiro Yoshida
{"title":"Non-adaptive estimation for degenerate diffusion processes","authors":"A. Gloter, Nakahiro Yoshida","doi":"10.1090/tpms/1207","DOIUrl":null,"url":null,"abstract":"We consider a degenerate system of stochastic differential equations. The first component of the system has a parameter \n\n \n \n θ\n 1\n \n \\theta _1\n \n\n in a non-degenerate diffusion coefficient and a parameter \n\n \n \n θ\n 2\n \n \\theta _2\n \n\n in the drift term. The second component has a drift term with a parameter \n\n \n \n θ\n 3\n \n \\theta _3\n \n\n and no diffusion term. Parametric estimation of the degenerate diffusion system is discussed under a sampling scheme. We investigate the asymptotic behavior of the joint quasi-maximum likelihood estimator for \n\n \n \n (\n \n θ\n 1\n \n ,\n \n θ\n 2\n \n ,\n \n θ\n 3\n \n )\n \n (\\theta _1,\\theta _2,\\theta _3)\n \n\n. The estimation scheme is non-adaptive. The estimator incorporates information of the increments of both components, and under this construction, we show that the asymptotic variance of the estimator for \n\n \n \n θ\n 1\n \n \\theta _1\n \n\n is smaller than the one for standard estimator based on the first component only, and that the convergence of the estimator for \n\n \n \n θ\n 3\n \n \\theta _3\n \n\n is much faster than for the other parameters. By simulation studies, we compare the performance of the joint quasi-maximum likelihood estimator with the adaptive and one-step estimators investigated in Gloter and Yoshida [Electron. J. Statist 15 (2021), no. 1, 1424–1472].","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

We consider a degenerate system of stochastic differential equations. The first component of the system has a parameter θ 1 \theta _1 in a non-degenerate diffusion coefficient and a parameter θ 2 \theta _2 in the drift term. The second component has a drift term with a parameter θ 3 \theta _3 and no diffusion term. Parametric estimation of the degenerate diffusion system is discussed under a sampling scheme. We investigate the asymptotic behavior of the joint quasi-maximum likelihood estimator for ( θ 1 , θ 2 , θ 3 ) (\theta _1,\theta _2,\theta _3) . The estimation scheme is non-adaptive. The estimator incorporates information of the increments of both components, and under this construction, we show that the asymptotic variance of the estimator for θ 1 \theta _1 is smaller than the one for standard estimator based on the first component only, and that the convergence of the estimator for θ 3 \theta _3 is much faster than for the other parameters. By simulation studies, we compare the performance of the joint quasi-maximum likelihood estimator with the adaptive and one-step estimators investigated in Gloter and Yoshida [Electron. J. Statist 15 (2021), no. 1, 1424–1472].
退化扩散过程的非适应性估计
我们考虑一个退化的随机微分方程系统。系统的第一个分量的非退化扩散系数有一个参数 θ 1 \theta _1,漂移项有一个参数 θ 2 \theta _2。第二个分量的漂移项参数为 θ 3 \theta _3,没有扩散项。在采样方案下讨论了退化扩散系统的参数估计。我们研究了 ( θ 1 , θ 2 , θ 3 ) (\theta _1,\theta _2,\theta _3) 的联合准极大似然估计器的渐近行为。估计方案是非适应性的。在这种结构下,我们发现θ 1 \theta _1的估计值的渐近方差小于仅基于第一个分量的标准估计值的渐近方差,而且θ 3 \theta _3的估计值的收敛速度远快于其他参数。通过模拟研究,我们比较了联合准极大似然估计器与 Gloter 和 Yoshida [Electron. J. Statist 15 (2021),no. 1,1424-1472] 中研究的自适应估计器和一步估计器的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.30
自引率
0.00%
发文量
22
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信