权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Statistical interence based on studentized robust statistics

基于学生化稳健统计的统计干预

基本信息

批准号：
10640129
负责人：
SHIRAISHI Takaaki
金额：
$ 0.64万
依托单位：
Yokohama City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

We considered two-sample and multivariate two-way manova model included in YィイD2iィエD2=h(xィイD2iィエD2,θ) + εィイD2iィエD2, i=1,・・・, n,θ∈Θ where εィイD2iィエD2, i=1, ・・・, n, are mutually independent and identically distributed with a p-variate continuous distribution function F(x,Σ) having null mean and finite positive definite variance-covariance matrix Σ. In pratical applicational model assumptions, the scale-parameter of the underlying distribution is unknown and Fisher's consistency does not hold. We need to construct flexible statistical procedures. So scale invariant statistical procedures based on M-statistics were proposed. Their asymptotic noncentral xィイD12ィエD1-distributions for testing homogeneity were drawn under a contiguous sequence of location-alternatives without assuming Fisher consistency : ∫ψィイD2lィエD2(xィイD1(l)ィエD1)dFィイD2lィエD2(xィイD1(l)ィエD1)=0. Asymptotic robustness was derived. The permutation tests based on the proposed M-test statistics were considered. Using a Monte Carlo simulation, their power was compared with permutation tests based on parametric test statistics. Next robust estimators for location parameters were proposed, based on studentized M-statistics. The asymptotic normality of these estimators was drawn. After a simple algorithm was studied, the risks of the M-estimators and the least squares estimators were compared due to a simulation. For a univariate case, it was found that (i) the asymptotic relative efficiency (ARE) of the proposed M-procedures relative to parametric procedures agreed with the ARE of one-sample M-estimator proposed by Huber (1964) relative to the sample mean, and that (ii) for small sample sizes, the M-procedures were more efficient than parametric procedures except the case that an underlying distribution is normal.Moreover many computer soft programs were created and shrinkage estimators were discussed.

本文考虑了两样本多变量双向双方差模型Y_（？）D_（？）D_（？）D_（？）=h（x_（？）D_（？）D_（？）D_（？），θ）+ ε_（？）D_（？）D_（？）D_（？）D_（？），i = 1，···，n，θ∈Θ，其中ε_（？）D_（？）D_（？）D_（？）D_（？）D_（？）D_（？），i=1，···，n，n，相互独立，同分布，p-变量连续分布函数F（x，n）具有零均值和有限正定的方差-协方差矩阵。在实际应用模型假设中，底层分布的尺度参数是未知的，Fisher的一致性不成立。我们需要建立灵活的统计程序。因此，提出了基于M-统计量的尺度不变统计方法。在不假设Fisher一致性的情况下，在连续的位置选择序列下绘制了检验同质性的渐近非中心x D12 D1分布：D2 l D2（x D1（l）D1）dF D2 l D2（x D1（l）D1）=0。渐近鲁棒性。考虑了基于M检验统计量的排列检验。使用蒙特卡罗模拟，他们的权力进行了比较，置换检验的基础上参数检验统计。其次，基于学生化M-统计量，提出了位置参数的稳健估计。这些估计量的渐近正态性。在研究了一种简单算法后，通过仿真比较了M-估计量和最小二乘估计量的风险。对于单变量情形，我们发现：（i）所提出的M-方法相对于参数方法的渐近相对效率（ARE）与Huber（1964）提出的单样本M-估计量相对于样本均值的ARE一致;（ii）对于小样本情形，M-除了基本分布是正态分布的情况外，参数方法比参数方法更有效。此外，许多计算机软件程序被创建，讨论了收缩估计量。