Distributed testing on mutual independence of massive multivariate data

Abstract

The article considers a distributed divide-and-conquer method to test the mutual independence between components of massive multivariate data. In particular, a new test statistic based on U-statistics by dividing the full data samples into disjoint blocks will be established. Some numerical simulations and real data analysis demonstrate that the proposed method is effective, and it can significantly reduce the computational complexity and save the running time of the test procedure on massive data inference.

Keywords:

• Mutual independence
• divide-and-conquer method
• symmetric measure
• computation complexity

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H15
• Secondary 62G10

Acknowledgments

The authors would like to thank the referee and an associate editor for their constructive comments and suggestions that have led to improvements in the article.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Grant No. 11401169) and Natural Science Foundation of Henan Province of China (Grant No. 202300410089).