Validation of positive expectation dependence

Abstract

In this paper, we develop tests for positive expectation dependence. The proposed tests are based on weighted Kolmogorov−Smirnov type statistics. These originate from the function valued monotonic dependence function, describing local changes of the strength of the dependence. The resulting procedure is supported by a simple and insightful graphical device. This paper presents asymptotic and simulation results for such tests. We show that an inference relying on p-values and wild bootstrap allows to overcome inherent difficulties of this testing problem. Our simulations show that the new tests perform well in finite samples. A Danish fire insurance data set is examined to demonstrate the practical application of the proposed inference methods.

Testing for more positive expectation dependence with application to model comparison

“…for some z. Tests for expectation dependance have been proposed in Zhu et al (2016), Cmiel and Ledwina (2017) and Linton et al (2018). Guo and Li (2016) proposed a method to construct uniform confidence band for quantities defining expectation dependence, derived from Hoeffding's inequality.…”