期刊
BIOMETRIKA
卷 104, 期 1, 页码 129-139出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asw071
关键词
Bayes factor; Coefficient of determination; Hypothesis test; Likelihood ratio
资金
- U.S. National Science Foundation
- National Institutes of Health
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1613035] Funding Source: National Science Foundation
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.
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