Improvement of the nonparametric statistical inference under complex statistical model and its application

复杂统计模型下非参数统计推断的改进及其应用

• 批准号: 16340026
• 负责人: MAESONO Yoshihiko
• 金额: $ 7.03万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340026/
• 关键词: Asymptotic theory of inference; Normalizing transformation; Resampling method; Non-linear modeling; Functional data analysis; Dynamic programming; Multiple decision problem; Diffusion process; カーネル型推定量; 確率点推定; 黄金双対; 非線形混合モデル; マルコフ過程; 漸近確率展開 /

For the data which has complex structure, like genome or financial data, we have to modify or improve ordinal statistical methods. Our purpose of this project is to propose new methods and study basic properties of the new methods under nonparametric setting. We obtain the following results. 1. Without assuming the underlying distribution, we obtain asymptotic representations of inversions of the Cornish-Fisher approximation and normalizing transformation. Using these representations, we compare mean squared errors of the inversions, theoretically. We also propose new confidence intervals that improve the ordinal method. 2.Based on the Bayes approach, we obtain new information criteria. Applying the new criteria to complex statistical model, we obtain new statistical methods which improve accuracy of statistical inference. We also propose new regularized basis expansions, and obtain theoretical properties of them. 3.We propose new confidence region of difference between mean vectors of bivariate normal distributions. This confidence region is based on the sequential method, and using mathematical programming approach, we prove that the new region is superior to ordinal region. 4.Under the uncertainty, we introduce Markov model, and study optimality based on non-additive stochastic dynamic programming. Using embedded method, we also prove optimality when the criterion is non-linear, and show that those results are applicable to the statistical inference. 5.For discretely observed diffusion process, we obtain new statistical inference methods, based on approximate martingale stochastic equation. We also propose a new estimator of a drift parameter for diffusion process with small variation, and prove consistency and asymptotic normality of the new estimator.

对于具有复杂结构的数据，如基因组或金融数据，我们必须修改或改进顺序统计方法。本项目的目的是提出新的方法，并研究新方法在非参数设置下的基本性质。我们得到了以下结果。1.在不假定基本分布的情况下，我们得到了Corish-Fisher近似和正规化变换的逆的渐近表示。使用这些表示法，我们从理论上比较了反演的均方误差。我们还提出了新的可信区间，改进了序数方法。2.基于贝叶斯方法，得到了新的信息准则。将新准则应用于复杂统计模型，得到了新的统计方法，提高了统计推断的准确性。我们还提出了新的正则化基展开式，并得到了它们的理论性质。3.提出了二元正态分布均值向量之差的新置信域。该置信域是基于序贯方法的，并利用数学规划的方法证明了新的置信度区域优于序数区域。4.在不确定条件下，引入马尔可夫模型，研究了基于非加性随机动态规划的最优性。利用嵌入方法，我们还证明了当准则为非线性时的最优性，并证明了这些结果适用于统计推断。5.对于离散观测的扩散过程，我们得到了基于近似鞅随机方程的新的统计推断方法。我们还提出了一个小偏差扩散过程漂移参数的新估计，并证明了新估计的相合性和渐近正态性质。

项目成果

Confidence regions of parameters in a nonlinear repeated measurementmodel with mixed effects

具有混合效应的非线性重复测量模型中参数的置信区域

• 发表时间: 2007
• 期刊: Hiroshima Mathematical Journal Vol.37
• 作者: BABA;Yuko;et. al.
• 通讯作者: et. al.

Fixed width confidence interval for equal means with intraclasscorrelation model

具有类内相关模型的等均值的固定宽度置信区间

• 发表时间: 2006
• 期刊: SUT, Journal of Mathematics vol.42
• 作者: HYAKUTAKE;Hiroto;et. al.
• 通讯作者: et. al.

Information Criteria and Statistical Modeling, Springer

信息标准和统计建模，施普林格

• 发表时间: 2008
• 作者: S.;Konishi;et. al.;M.Tabata;S.KOIVISHI and G.H-TAGAWA
• 通讯作者: S.KOIVISHI and G.H-TAGAWA

An Edgeworth expansion and a normalizing transformation for L-statistics

L 统计量的埃奇沃斯展开和归一化变换

• 发表时间: 2007
• 期刊: Bulletin of Informatics and Cybernetics 39
• 作者: 馮偉;小和田正;Y. Maesono
• 通讯作者: Y. Maesono

A dynamic pricing of exotic options

奇异期权的动态定价

• 发表时间: 2004
• 期刊: Proceedings of The First International Workshop on Intelligent Finance(IWIF1) 1
• 作者: Seiichi Iwamoto;Seiishi Iwamoto
• 通讯作者: Seiishi Iwamoto