数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 907-918.doi: 10.1016/S0252-9602(10)60088-4

• 论文 • 上一篇    下一篇

DISPERSION COMPARISONS OF TWO PROBABILITY VECTORS UNDER MULTINOMIAL SAMPLING

熊世峰, 李国英   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2007-10-08 修回日期:2008-05-12 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    Sponsored by the National NSFC (10771126, 10801130)

DISPERSION COMPARISONS OF TWO PROBABILITY VECTORS UNDER MULTINOMIAL SAMPLING

 XIONG Shi-Feng, LI Guo-Ying   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2007-10-08 Revised:2008-05-12 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    Sponsored by the National NSFC (10771126, 10801130)

摘要:

We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and
consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.

关键词: Multinomial distribution, dispersion, diversity,  bootstrap, hypothesis testing, majorization

Abstract:

We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and
consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.

Key words: Multinomial distribution, dispersion, diversity,  bootstrap, hypothesis testing, majorization

中图分类号: 

  • 62F03