Independence test in high-dimension using distance correlation and power enhancement technique

Abstract

This paper is concerned with independence test in high-dimension. A new test statistic is proposed with two terms: one is based on the modified distance correlation statistic, the other is constructed to enhance the power under sparse alternatives. Asymptotic properties of the test statistic are discussed under some regular conditions. The finite-sample simulations exhibit its superiority over some existing procedures. Finally, a real data example illustrates the proposed test.

Keywords:

• Distance correlation
• independence test
• high-dimension
• power enhancement technique

Acknowledgments

The authors would like to thank the Editor and the referees for their constructive comments which have greatly improved the earlier versions of this paper, and also to thank Prof. Hengjian Cui for his encouragement, valuable suggestions, and strict guidance.

Additional information

Funding

Dr. Guo’s research is supported by China Postdoctoral Science Foundation (2017M620827, 2018T110118), Beijing Postdoctoral Research Foundation, National Natural Science Foundation of China (NNSFC)(grants 11471223, 11231010, 11071022), Capacity Building for Sci-Tech Innovation - Fundamental Scientific Research Funds (Nos. 025185305000/204, 19530050181) and Youth Innovative Research Team of Capital Normal University.