Generalized R-squared for detecting dependence

• 成果类型: Article
• 署名作者: Wang, X.; Jiang, B.; Liu, J. S.
• 署名单位: Harvard University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw071
• 发表日期: 2017
• 页码: 129139
• 关键词: INDEPENDENCE; regression

摘要

Detecting 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.