Title: Validation of positive expectation dependence
Authors: Bogdan Cmiel - Polish Academy of Sciences (Poland) [presenting]
Teresa Ledwina - Polish Academy of Sciences (Poland)
Abstract: There is quickly growing evidence that dependence structure of observed random vectors can not be neglected in a reliable data analysis. Extensive work of practitioners has revealed that some well-known notions as for example the correlation coefficient are not sufficient to explain complex character of many relations while some other existing or new notions can be much more useful in nowadays practice and some specific applications. Last years increasing role of the notion of positive expectation dependence has been observed in different research areas. Tests are developed for such type of dependence. The solutions are weighted Kolmogorov-Smirnov type statistics. They originate from the function valued monotonic dependence function, describing local changes of the strength of the dependence. Therefore, the inference can be supported by a simple and insightful graphical device. An asymptotic and simulation results for such tests are presented. It is shown that an inference relying on $p-$values and wild bootstrap allows to overcome inherent difficulties of this testing problem. Some simulations show that the new tests perform well in finite samples.