Exploratory statistical theory after searching the underlying distribution

搜索潜在分布后的探索性统计理论

基本信息

  • 批准号:
    16540112
  • 负责人:
  • 金额:
    $ 1.02万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2004
  • 资助国家:
    日本
  • 起止时间:
    2004 至 2006
  • 项目状态:
    已结题

项目摘要

1. As statistical estimation procedures for location, the sample mean, Hodges and Lehman's R-estimator, and Huber's M-estimator are introduced in a one-sample model. The asymptotic distributional theory for the three estimators and simulated mean squared errors give the features of the respective estimators depending on the underlying distribution. Based on the features, we propose an estimation procedure selecting one of the three estimators after searching a distribution near to the underlying distribution. It is shown that the mean squared error of the new estimator is more stable than the three estimators. Next, as distribution-free test procedures, the conditional t-test, Wilcoxon's signed rank test, and the M-test are introduced. Asymptotic relative efficiency and simulated power of the respective tests are investigated. Based on their features, we propose a stable test procedure selecting one of the three tests after searching a distribution near to the underlying distribution.2 … More . In a one-way analysis of variance model, robust versions based on scale-invariant M-statistics are proposed for single-step multiple comparisons procedures discussed by Tukey (1953), Dunnett (1955), and Scheffe (1953). Although the distributions for the normal theory pocedures are given by double integrals, the asymptotic distributions for the proposed procedures are expressed as single integrals. Tables of asymptotic critical values are provided for the proposed M procedures. Furthermore although the symmetry of the underlying distribution is needed in the asymptotic theory of Huber's M-estimators, the proposed procedures do not demand the symmetry. It is found that the M-procedures are superior to the classical normal theory procedures except the case that an underlying distribution is normal.3. In the one-way layout assuming that the underlying distribution is normal, we may execute Tukey-Kramer multiple comparisons procedure for searching all pairwise differences of locations. For the unequal sample sizes, the Tukey-Kramer (T-K) method is conservative. The T-K method is given by using the upper c point of the studentized range distribution A(t). A(t) is a lower bound for the distribution of the Tukey-Kramer statistic. We derive the distribution B(t) which gives an upper bound for the distribution of Tukey-Kramer statistic. By using numerical double integration, we show that the value of B(t) is a little larger than that of A(t). As the result, we may verify that the conservativeness of the T-K method is small. Less
1. 作为位置的统计估计程序,在单样本模型中引入了样本均值、Hodges 和 Lehman 的 R 估计器以及 Huber 的 M 估计器。三个估计量的渐近分布理论和模拟均方误差根据基础分布给出了各个估计量的特征。基于这些特征,我们提出了一种估计过程,在搜索接近基础分布的分布后选择三个估计器之一。结果表明,新估计器的均方误差比三个估计器更稳定。接下来,作为无分布检验程序,介绍条件t检验、Wilcoxon符号秩检验和M检验。研究了各个测试的渐近相对效率和模拟功效。根据它们的特征,我们提出了一种稳定的测试程序,在搜索接近基础分布的分布后选择三个测试之一。2 …更多。在方差模型的单向分析中,针对 Tukey (1953)、Dunnett (1955) 和 Scheffe (1953) 讨论的单步多重比较程序提出了基于尺度不变 M 统计量的鲁棒版本。虽然正态理论程序的分布是由二重积分给出的,但所提出的程序的渐近分布表示为单积分。为建议的 M 过程提供了渐近临界值表。此外,尽管 Huber M 估计量的渐近理论中需要基础分布的对称性,但所提出的过程并不要求对称性。结果表明,除了基础分布为正态分布的情况外,M-过程优于经典正态理论过程。 3.在单向布局中,假设基础分布是正态分布,我们可以执行 Tukey-Kramer 多重比较过程来搜索位置的所有成对差异。对于不相等的样本量,Tukey-Kramer (T-K) 方法是保守的。 T-K 方法是通过使用学生化极差分布 A(t) 的上 c 点给出的。 A(t) 是 Tukey-Kramer 统计量分布的下界。我们推导出分布 B(t),它给出了 Tukey-Kramer 统计量分布的上限。通过数值二重积分,我们发现 B(t) 的值略大于 A(t) 的值。由此,我们可以验证T-K方法的保守性很小。较少的

项目成果

期刊论文数量(28)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Asymptotic confidence intervals based on M-procedures in one- and two-sample models
一样本和两样本模型中基于 M 过程的渐近置信区间
The upper bound for the distribution of Tukey-Kramer's statistic
Tukey-Kramer 统计量分布的上限
Estimation of a normal covariance matrix parametrized by irreducible symmetric cones under Stein's loss
Stein 损失下不可约对称锥参数化的正态协方差矩阵的估计
Improving on the sample covariance matrix for a complex elliptically contoured distribution
改进复杂椭圆轮廓分布的样本协方差矩阵
Altenative estimators of the commom regression matrix in two GMANOVA models under weighted quadratic losses
加权二次损失下两个 GMANOVA 模型中公共回归矩阵的替代估计
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SHIRAISHI Takaaki其他文献

SHIRAISHI Takaaki的其他文献

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{{ truncateString('SHIRAISHI Takaaki', 18)}}的其他基金

Multiple comparison procedures based on robust statistics
基于稳健统计的多重比较程序
  • 批准号:
    20540126
  • 财政年份:
    2008
  • 资助金额:
    $ 1.02万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Statistical interence based on studentized robust statistics
基于学生化稳健统计的统计干预
  • 批准号:
    10640129
  • 财政年份:
    1998
  • 资助金额:
    $ 1.02万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

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