Wang, XJiang, BLiu, Jun2017-11-292017Wang, X., B. Jiang, and J. S. Liu. 2017. "Generalized R-squared for detecting dependence." Biometrika 104, no. 1: 129-139. doi: 10.1093/biomet/asw0710006-3444http://nrs.harvard.edu/urn-3:HUL.InstRepos:34391707Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimators are among the most powerful test statistics compared with several state-of-the-art methods.en-USJournal Article2017-11-2910.1093/biomet/asw071