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Some contributions to inference based on spacings.

机译：对基于间距的推断的一些贡献。

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摘要

Tests for goodness-of-fit and for some problems in reliability based on U-statistics of the spacings, as well as higher-order spacings, are studied here. The standard large-sample theory of U -statistics does not apply here, because spacings are dependent variables. However under the null hypothesis, the U-statistics based on such spacings are distributionally equivalent to a U -statistic based on independent quantities, conditional on an average of such quantities. This can be used to derive the relevant large-sample theory.;The asymptotic distribution theory under both the null hypothesis and a sequence of close alternatives, is developed. The generalized Gini tests based on spacings is an important example of a U-statistic of this type. Such a Gini test is analogous to Rao's spacings test. It is found that the second-order Gini test is the asymptotically most powerful test of its class, and has the same efficacy of the Greenwood statistic. For higher-order spacings, a similar result is shown to be true.;The final part of the thesis investigates some testing problems in reliability theory. We study the problem of testing Exponentiality against the alternative of increasing failure rate. A weighted U-statistic based on the spacings formed by the empirical scaled TTT-transform is proposed. The test is based on the mean sign difference of the normalized spacings, and is shown to have quite favorable performance based on Monte Carlo powers. We conclude with some open problems as e.g. finding the asymptotic distribution theory for weighted U-statistics of this genre.
机译：本文研究了基于间隔和更高阶间隔的U统计量的拟合优度和某些可靠性问题的测试。 U统计学的标准大样本理论在这里不适用，因为间隔是因变量。然而，在零假设下，基于这种间隔的U统计量在分布上等效于基于独立数量的U统计量，其条件是此类量的平均值。这可以用来推导相关的大样本理论。在零假设和一系列紧密选择的同时，建立了渐近分布理论。基于间距的广义Gini检验是此类U统计量的重要示例。这种基尼检验类似于Rao的间距检验。发现二阶基尼检验是同类渐近最有效的检验，并且具有与格林伍德统计量相同的功效。对于高阶间距，也显示出相似的结果。;本文的最后部分研究了可靠性理论中的一些测试问题。我们研究了针对故障率增加的替代方案测试指数性的问题。提出了一种基于经验缩放的TTT变换所形成的间隔的加权U统计量。该测试基于归一化间距的均值符号差，并基于蒙特卡洛幂显示出相当不错的性能。我们总结了一些未解决的问题，例如寻找该类型的加权U统计量的渐近分布理论。

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  • 作者

    Tung, David Deming.;

  • 作者单位

    University of California, Santa Barbara.;

  • 授予单位 University of California, Santa Barbara.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 77 p.
  • 总页数 77
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-17 11:38:19

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