Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation

摘要: It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures bivariate data. Other scalar measures capable of capturing exist. A common disadvantage such measures, however, they cannot distinguish between negative and positive dependence, typically alternative hypothesis accompanying test independence simply "dependence". This paper discusses how a newly developed local measure, Gaussian correlation, can be used construct global tests independence. measure constructed by aggregating on subsets $\mathbb{R}^{2}$ , an proposed. Choice bandwidth based likelihood cross-validation. Properties this asymptotics corresponding estimate are discussed. bootstrap version implemented tried out both real simulated The performance proposed compared Brownian distance covariance test. Finally, when rejected, investigate cause rejection.