| 戴家佳,杨爱军.改进卡方检验[J].数学研究及应用,2009,29(1):113~123 |
| 改进卡方检验 |
| A Modified Chi-Squared Goodness-of-Fit Test |
| 投稿时间：2008-03-26 修订日期：2008-04-18 |
| DOI：10.3770/j.issn:1000-341X.2009.01.015 |
| 中文关键词: Pearson卡方检验 Von Mises-Fisher分布 Watson分布 方向数据. |
| 英文关键词:Pearson's chi-squared test Von Mises-Fisher distribution Watson distribution vectorial data. |
| 基金项目:北京市自然科学基金(N0.1062001); 北京市属市管高等学校人才强教计划(N0.05006011200702) |
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| 中文摘要: |
| Pearson卡方拟合优度检验的结果依赖于对样本空间的划分，不同的划分可能会得到不同的推断结果.本文提出了一个改进的拟合优度卡方检验，它克服了Pearson卡方检验依赖分组的弱点.并将改进卡方检验应用于检验方向数据是否来自球面上的均匀分布.模拟结果表明：改进卡方检验有较高的检验功效并且是稳健的. |
| 英文摘要: |
| In goodness-of-fit tests, Pearson's chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson's chi-squared test depends on the partition of the sample space. Different constructions of the partition of the sample space may lead to different conclusions. Based on an equiprobable partition of sample space, a modified chi-squared test is proposed. A method for constructing the modified chi-squared test is proposed. As an application, the proposed test is used to test whether vectorial data come from an uniformity distribution defined on the hypersphere. Some simulation studies show that the modified chi-squared test against different alternative is robust. |
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