Validation of positive expectation dependence

Ćmiel, Bogdan; Ledwina, Teresa

ESAIM: Probability and Statistics, Tome 21 (2017), pp. 536-561.

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.

Classification : 60F05, 62G09, 62G10, 62G20
Mots clés : Hypothesis testing, expectation dependence, Lorenz curve, monotonic dependence function, multiplier central limit theorem, wild bootstrap, Zenga curve

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