November 15, 2019
Joint CORE/ISBA seminar
A projection pursuit approach for robust maximum association measures with an extension for sparsity
Andreas Alfons, Erasmus Universiteit Rotterdam, The Netherlands
Abstract : The maximum association between two multivariate random variables X and Y is defined as the maximal value that a bivariate association measure between one-dimensional projections a'X and b'Y can attain. Rather than taking the Pearson correlation as projection index, we suggest to use more robust association measures such as the Spearman or Kendall correlation. We present a projection-pursuit algorithm, study the robustness properties of the resulting maximum association measures, and underline the theoretical results with numerical experiments. Moreover, we present an extension of the algorithm that allows for sparse estimation of the weighting vectors a and b in order to increase the interpretability of the results in higher dimensions. In addition, we demonstrate how the proposed algorithms can be applied in the statistical computing environment R using our add-on package ccaPP.