Testing independence based on Spearman’s footrule in high dimensions

Abstract.

Spearman’s footrule is a widely used tool to discover the relationship between two continuous random variables, mainly because of its robustness, natural interpretation, and simplicity of calculation. In this article, we propose a new test statistic based on the sum of squares of pairwise Spearman’s footrule, to test the mutual independence of a high dimensional random vector. The large sample properties of the proposed test method are established. Simulation results show that the new test has higher power than existing test methods under some circumstances. An example with real life data is discussed to illustrate the usefulness and effectiveness of the proposed test statistic.

Keywords:

• High dimensions
• complete independence
• Spearman’s footrule
• rank correlation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11971045 and 12271014), Young Talent program of Beijing Municipal Education Commission (No. CIT & TCD201904021), and the Science and Technology Project of Beijing Municipal Education Commission (No. KM202210005012).