The improved correlation coefficient of Chatterjee

Chatterjee's new coefficient proposed by Chatterjee [2021, ‘A New Coefficient of Correlation’, Journal of the American Statistical Association, 116(536), 2009–2022.] is used to measure the degree of dependence between two scalars by rank correlation. However, the independence test based on Chatterjee's rank correlation may lose power since it only considers the distance between the nearest neighbours and ignores the other neighbours. In this paper, we propose an improvement to Chatterjee's new coefficient by incorporating the inverse distance-weighting, and further obtain the asymptotic normality of the improved coefficient and the Berry–Esseen bound under the null hypothesis. The proposed method is evaluated on the simulated as well as the real data on Yeast Gene Expression. The results show that the proposed method is superior to Chatterjee's new coefficient under various alternative hypotheses.