Developing statistical asymptotic theory for jump processes and its applications

发展跳跃过程的统计渐近理论及其应用

• 批准号: 23740082
• 负责人: MASUDA Hiroki
• 金额: $ 2.41万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740082/
• 关键词: 統計的漸近推測; ジャンプ過程; 確率過程論; 確率解析; 確率微分方程式モデル

Mainly, we have derived the following results concerning statistical inference for stochastic process models with jumps: (1) Asymptotic normality of the Gaussian quasi-likelihood type estimator together with an easy-to-use approximate confidence regions, when the model has general non-linear coefficients and non-Gaussian noise; (2) Model-free asymptotic distribution of a bias-corrected functional of residuals, with applications to noise-normality and diffusion-coefficient misspecification tests, when the model is of a general continuous-time regression type; (3) Asymptotic mixed normality of the least-absolute deviation estimator and the quasi-likelihood estimator based on the small-time stable approximation, when the noise process can be approximately non-Gaussian stable in small time. In particular, the proposed estimator in (3) is much more efficient than that in (1), while the model setting in (3) is more limited compared with that of (1).

主要得到了具有跳跃的随机过程模型的统计推断结果：(1)当模型具有一般非线性系数和非高斯噪声时，高斯拟似然型估计量的渐近正态性和易于使用的近似置信区域；(2)当模型为一般连续时间回归类型时，残差偏校正函数的无模型渐近分布，并应用于噪声正态性检验和扩散系数错配检验；(3)当噪声过程可以在小时间近似非高斯稳定时，基于小时间稳定近似的最小绝对偏差估计量和拟似然估计量的渐近混合正态性。特别是，(3)中提出的估计器比(1)中的估计器效率高得多，而(3)中的模型设置与(1)相比更有限。

项目成果

On estimating stable Ornstein-Uhlenbeck processes

关于估计稳定的 Ornstein-Uhlenbeck 过程

• 作者: A. Kohatsu-Higa;N. Vayatis;K. Yasuda;Shuya Chiba;酒井拓史;増田 弘毅
• 通讯作者: 増田 弘毅

Hiroki Masuda (personal webpage)

增田弘树（个人网页）

On statistical inference for Levy-driven models

Levy 驱动模型的统计推断

• 发表时间: 2013

Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes

离散观测随机过程的自归一化残差泛函的渐近

• DOI: 10.1016/j.spa.2013.03.013
• 发表时间: 2013
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: X. Huang;塩沢裕一;H. Masuda and N. Yoshida;渡部善隆,藤原宏志,中尾充宏;Kaoru Fujioka;H. Masuda;Kaoru Fujioka;Y. Iso and H. Fujiwara;Yuichi Shiozawa;H. Masuda
• 通讯作者: H. Masuda

On simulation of tempered stable random variates

• DOI: 10.1016/j.cam.2010.12.014
• 发表时间: 2010-03
• 期刊: J. Comput. Appl. Math.
• 作者: Ray Kawai;Hiroki Masuda