On relationships between Chatterjee’s and Spearman’s correlation coefficients
Document Type
Lecture
Publication Date
10-19-2023
Abstract
In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this talk, we will study the probabilistic relationships between Chatterjee’s correlation and the widely used Spearman’s correlation. We will show that, under independence, the two sample-based correlations are asymptotically joint normal and asymptotically independent. For dependent variables, we will establish some extremal cases featuring large differences between these two metrics. Motivated by these findings, a new independence test is proposed by combining Chatterjee’s and Spearman’s correlations into a maximal strength measure of variable association. We will use both simulated data and a real-world dataset to show the good sensitivity of the new test to different correlation patterns.
Relational Format
presentation
Recommended Citation
Zhang, Qingyang, "On relationships between Chatterjee’s and Spearman’s correlation coefficients" (2023). Probability & Statistics Seminar. 13.
https://egrove.olemiss.edu/math_statistics/13
