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

基本信息

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

项目摘要

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（例如基因组或财务数据）的数据，我们必须修改或改善顺序统计方法。该项目的目的是提出新方法并研究非参数设置下新方法的基本特性。我们获得以下结果。 1。在不假设基本分布的情况下，我们获得了康沃尔 - 法派近似和归一化转换的反转的渐近表示。使用这些表示形式，我们从理论上比较了反转的平方平方误差。我们还提出了改善序数方法的新置信区间。 2.基于贝叶斯方法，我们获得了新的信息标准。将新标准应用于复杂的统计模型，我们获得了新的统计方法，从而提高了统计推断的准确性。我们还提出了新的正则基础扩展，并获得了它们的理论特性。 3.我们提出了双变量正常分布的平均向量之间的新置信区域。该置信区域基于顺序方法，并使用数学编程方法，我们证明了新区域优于顺序区域。 4.在不确定性下，我们介绍了马尔可夫模型，并基于非加性随机动态编程的研究最佳性。使用嵌入式方法，当标准非线性时，我们还证明了最佳性，并表明这些结果适用于统计推断。 5.对于离散观察到的扩散过程，我们基于近似Martingale随机方程获得了新的统计推断方法。我们还提出了一个新估计值的新估计值，用于扩散过程，并证明了新估计量的一致性和渐近正态性。