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.
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^quared 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 chisquared test against different alternative is robust.
基金
Foundation item： the Natural Science Foundation of Beijing （No. 1062001）
Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality（No. 05006011200702）.
Acknowledgements The authors cordially thank the Associate Editor and Reviewers for their constructive comments which lead to improvement of the manuscript. They are also very grateful to Prof. Adelaide Figueiredo for his help.
关键词
数理统计
一般数理统计
概率论
回归理论
Pearson＇s chi-squared test
Von Mises-Fisher distribution
Watson distribution
vectorial data.
