turkmath.org

Distance correlation is a relatively new and powerful dependence measure with desirable properties. For example, distance correlation vanishes if and only if the variables are independent. In this talk, after introducing distance correlation and its properties, he will illustrate two applications. In the first application, we focus on the well-known variable selection problem in regression, which is the task of selecting the most influential predictors explaining the response and removing the others from the model. We propose a variable selection criterion based on distance correlation and illustrate the performance of the proposed method through comparative simulations, where the benchmark methods are stepwise AIC and lasso. In several cases with linear dependence, all methods turned out to be comparable. In the presence of nonlinear or uncorrelated dependencies, we observed that our proposed method may be favorable. In the second application, we use distance correlation as an alternative to the Mantel statistic, which is routinely used in many areas of ecology to measure the dependence between the elements in two resemblance matrices. We focus on resemblance matrices with nonlinear structures and point out that partial distance correlation is a powerful alternative to the Mantel statistic for measuring the association of such matrices.