Truncated correlation coefficient test for two random vectors

Abstract.

Measuring the correlation between two random variables is a classic problem in statistics. The common textbook measures are Pearson r, Spearman ρ, and Kendall τ correlation coefficients. These three values are especially useful for two univariate variables, although they have been extended to two random vectors such as RV, which is a linear correlation coefficient for two random vectors. In this article, we propose a truncated correlation coefficient measure to test whether two random vectors are independent, together with some statistical properties. We perform extensive simulation studies to compare powers of RV and the proposed test. Results show that the proposed test is more powerful than RV to detect the independence. Finally, two real data analyses further show the performance of the proposed test.

Keywords:

• Correlation
• independence
• Pearson r
• truncated point

Acknowledgment

To facilitate the usage for the proposed statistical test, the codes are available upon request by contacting with the corresponding author.

Disclosure statement

No competing financial interests exist.

Additional information

Funding

The work was supported by National Nature Science Foundation of China (12201432), Capital University of Economics and Business Newly Recruited Young Teachers Scientific Research Start-up Fund Project (No. XRZ2022066), and Capital University of Economics and Business Research Young Academic Innovation Team Fund Project (No. QNTD202207).