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Bootstrap methods with applications in multivariate analysis.

机译：Bootstrap方法及其在多变量分析中的应用。

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摘要

This study is concerned with certain classical methods in hypothesis testing and the construction of simultaneous confidence sets in multivariate linear analysis. Three approaches in hypothesis testings are proposed: Asymptotic, bootstrap, and prepivoting methods. The performance of the asymptotic method depends strongly on the availability of the asymptotic expansion. The asymptotic test statistic is first order correct. Although refinements to asymptotical tests have been shown to be second order accurate, they are too cumbersome for analytical approach. The bootstrap method, however, avoids such difficulties and can be approximated directly by a Monte Carlo algorithm. The principal aim of the present investigation is to compare the bootstrap method to the refinements of the asymptotic method in theory and in simulation. It is shown that the appropriate bootstrap test based on the Behrens-Fisher statistic is equivalent to James's (1954) first order asymptotic series and Yao's (1965) approximate degrees of freedom test; and the appropriate bootstrap likelihood ratio test automatically accomplishes Bartlett's adjustment to the chi-squared asymptotics. In addition, prepivoting any test statistic before forming a bootstrap test reduces the order of the error in rejection probability. The prepivoting can be iterated.; The problem of constructing simultaneous confidence sets in multivariate linear analysis is considered. In the case when the normality assumption does not satisfy, the classical methods such as pivotal method is too difficult for analytical approach. One way to improve this problem is to employ the nonparametric bootstrapping method that underlies Beran's (1988) bootstrapped roots method. Under stringent conditions, it is shown that the bootstrapped roots method overcomes distributional difficulties and generates simultaneous confidence sets such that the overall coverage probability is correct and the coverage probabilities of the individual confidence sets are equal in both multivariate regression and multivariate analysis of variance, respectively. For the special case in multivariate analysis of variance where the normality is presented, the projection method is proposed. It is shown that the projection method is not only suitable for balanced complete layout but also for the unbalanced complete layout.
机译：这项研究涉及假设检验中的某些经典方法以及多元线性分析中同时置信度集的构建。提出了三种假设检验方法：渐进法，自举法和前移法。渐近方法的性能在很大程度上取决于渐近展开的可用性。渐近检验统计量是一阶正确的。尽管对无症状测试的改进已被证明是二阶准确的，但对于分析方法而言却过于繁琐。但是，bootstrap方法避免了此类困难，并且可以通过Monte Carlo算法直接进行近似。本研究的主要目的是在理论上和仿真上将自举方法与渐近方法的改进进行比较。结果表明，基于贝伦斯－菲舍尔统计量的适当的自举检验等效于詹姆斯（1954）的一阶渐近级数和姚（1965）的近似自由度检验；适当的自举似然比测试将自动完成Bartlett对卡方渐近线的调整。另外，在形成自举测试之前预先确定任何测试统计量可以减少拒绝概率中的错误顺序。可以反复进行。考虑了在多元线性分析中构造同时置信度集的问题。在法向假设不满足的情况下，经典方法（例如枢轴方法）对于分析方法来说太困难了。解决此问题的一种方法是采用非参数自举方法，该方法是Beran（1988）自举根方法的基础。在严格条件下，证明了自举根法克服了分布困难并生成了同时置信度集，从而在多变量回归和多元方差分析中，总覆盖率均正确且各个置信度集的覆盖率均相等。针对方差多变量分析中出现正态性的特殊情况，提出了投影方法。结果表明，该投影方法不仅适用于平衡的完整布局，而且还适用于不平衡的完整布局。

著录项

  • 作者

    Zhu, Shuying.;

  • 作者单位

    University of California, Davis.;

  • 授予单位 University of California, Davis.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 110 p.
  • 总页数 110
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;
  • 关键词

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