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Consistency of Chi-squared test with varying number of classes
  • ISSN号：1009-6124
  • 期刊名称：Journal of Systems Science and Complexity
  • 时间：0
  • 页码：-
  • 分类：O212.1[理学—概率论与数理统计;理学—数学] O121.4[理学—数学;理学—基础数学]
  • 作者机构：[1]College of Mathematic and Statistics, Jishou University, Jishou 416000, China, [2]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China, [3]Department of Statistics, School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.
  • 相关基金：This research was supported by the Natural Science Foundation of China under Grant Nos. 11071022, 11028103, 11231010, 11471223, BCMIIS and the Beijing Municipal Educational Commission Foundation under Grant Nos. KZ201410028030, KM201210028005, and Jishou University Subject in 2014 （No： 14JD035）.
  • 相关项目：稳健变量选择与高维数据分析
作者： Huang Rui|Cui Hengjian|
关键词： 卡方检验, 一致性, 检验统计量, 同数, 同时检验, 渐近性质, 随机变量, 收敛速度, Consistency of chi-squared test, goodness of fit test, varying number of classes.
中文摘要：

合适的测试的古典摆平 chi 的美德假设班的数字被修理，同时，测试统计数值在空假设下面有限制 chi 平方分布。在测试与样品尺寸变化的班的数字依附越来越多的注意，是众所周知的。处于这种状况，然而，如此的摆平 chi 的测试统计数值的 asymptotic 性质没有理论结果。这份报纸与在一些条件下面改变班的数字证明摆平 chi 的测试的一致性。同时，作者也给在测试统计数值和相应 chi 平方之间的 Kolmogorov-Simirnov 距离的集中率分布式的随机的变量。另外，一个真实例子和模拟结果与改变班的数字验证理论结果的 reasonability 和摆平 chi 的测试的优势。

英文摘要：

The classical chi-squared goodness of fit test assumes the number of classes is fixed, meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis. It is well known that the number of classes varying with sample size in the test has attached more and more attention. However, in this situation, there is not theoretical results for the asymptotic property of such chi-squared test statistic. This paper proves the consistency of chi-squared test with varying number of classes under some conditions. Meanwhile, the authors also give a convergence rate of Kolmogorov- Simirnov distance between the test statistic and corresponding chi-square distributed random variable. In addition, a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125