Some multivariate goodness-of-fit tests based on data depth

Abstract

Based on data depth, three types of nonparametric goodness-of-fit tests for multivariate distribution are proposed in this paper. They are Pearson’s chi-square test, tests based on EDF and tests based on spacings, respectively. The Anderson–Darling (AD) test and the Greenwood test for bivariate normal distribution and uniform distribution are simulated. The results of simulation show that these two tests have low type I error rates and become more efficient with the increase in sample size. The AD-type test performs more powerfully than the Greenwood type test.

Keywords:

• multivariate goodness-of-fit test
• data depth
• Kolmogrov–Sminorv test
• Anderson–Darling statistic
• multivariate spacings

2000 AMS Subject Classification :

• Primary: 62G20
• Secondary: 62G10
• 60H10

Acknowledgements

The authors thank the anonymous referees for their constructive and helpful comments greatly. The work is supported by Humanities and Social Science Foundation of Ministry of Education of China (10YJC90011) and National Natural Science Foundation of China (11101362, 11071213).