Theory of Statistical Inference for Stochastic Processes and its Application to Mathematical Finance

随机过程统计推断理论及其在数学金融中的应用

• 批准号: 15500192
• 负责人: SAKAMOTO Yuji
• 金额: $ 2.18万
• 依托单位: Hiroshima International University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15500192/
• 关键词: Diffusion Process; Asymptotic Expansion; Markovian Process; M-estimator; degeneracy; Shrinkage Estimator; Discriminant Analysis; 拡散過程; ウィナー汎関数; マリアバン解析; 展開公式; マルコフ過程

(1)In the case where degenerate components are involved with a random variable of interest, we proved the validity of its distributional asymptotic expansion, and applied the result to the third order asymptotic expansion of the maximum likelihood estimator for the Ornstein-Uhlenbeck process.(2)As for the prediction problem, by using expansion formula for the generalized Wiener functional, we showed the Stein phenomenon, i.e., the prediction region centered at a shrinkage type estimator is better than that centered at a usual sample mean.(3)For functionals of Markovian process with a mixing property, we derived general and explicit formulas of distributional asymptotic expansion with a error bound, and used them to obtain a third order asymptotic expansion of the M-estimator for a general statistical model. As a typical application, we present third order asymptotic expansions of M or minimum contrast estimators for diffusion processes.(4)In order to approximate closely to the probabilities of mis-discrimination, we calculated asymptotic expansions for Bayes, plug-in, likelihood ratio type discrimination rules, and studied their numerical accuracies by Monte-Carlo experiments to show that our results gives very close approximations.

（1）如果退化成分与感兴趣的随机变量相关，我们证明了其分布渐近扩张的有效性，并将结果应用于三阶渐近扩展的最大可能性估计仪的最大可能性估计仪的渐近估计剂的最大可能性估计器的最大可能性估计剂的范围。即，以收缩型估计量为中心的预测区域比以通常的样本平均值为中心。（3）Markovian工艺具有混合属性的功能，我们得出了与错误绑定的分布渐近扩展的一般和明确的公式，并使用它们绑定了，并使用它们来获得三阶级别的近端模型的近三级均匀模型。作为典型的应用，我们提出了扩散过程中M或最小对比度估计器的三阶渐近扩展。（4）为了与差异歧视的概率紧密近似，我们计算了贝叶斯的渐近扩展，插入式，插件，可能性比率类型歧视规则，并通过monte-carements进行了实验，并对其进行了数字精确的实验。

项目成果

Expansions of the Coverage Probabilities of Prediction Region Based on a Shrinkage Estimator

基于收缩估计器的预测区域覆盖概率扩展

• 发表时间: 2004
• 期刊: Statistics 38
• 作者: Sakamoto;Y.
• 通讯作者: Y.

Sakamoto, Y., Yoshida, N.: "Asymnptotic Expansion under degeneracy"Journal of Japan Statistical Society. 33・2. 145-156 (2003)

Sakamoto, Y., Yoshida, N.：“简并下的渐近扩张”日本统计学会杂志 33・2（2003 年）。

Asymptotic Expansion Formulas for Functionals of e-Markov Processes with a Mixing Property

具有混合性质的e-Markov过程泛函的渐近展开式

• 发表时间: 2004
• 期刊: Ann.Inst.Statist.Math. 56-3
• 作者: Sakamoto;Y.
• 通讯作者: Y.

Asymptotic Expansion Formulas for Functionals of ε-Markoy Processes with a Mixing Property

具有混合性质的ε-Markoy过程泛函的渐近展开式

• 发表时间: 2004
• 期刊: Ann.Inst.Statist.Math. 56-3
• 作者: Sakamoto;Y.;Yoshida;N.
• 通讯作者: N.

Expansions of the Coverage Probabilitiesof Prediction Region Based on a Shrinkage Estimator

基于收缩估计器的预测区域覆盖概率扩展

• 发表时间: 2004
• 期刊: Statistics 38
• 作者: Sakamoto;Y.
• 通讯作者: Y.