A Modified Chi-Squared Goodness-of-Fit Test
Received:March 26, 2008  Revised:April 18, 2008
Key Word: Pearson's chi-squared test   Von Mises-Fisher distribution   Watson distribution   vectorial data.  
Fund ProjectL: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).
Author NameAffiliation
DAI Jia Jia College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
College of Science, Guizhou University, Guizhou 550025, China 
YANG Ai Jun College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.01.015
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