| Issue |
ESAIM: PS
Volume 21, 2017
|
|
|---|---|---|
| Page(s) | 536 - 561 | |
| DOI | https://doi.org/10.1051/ps/2017015 | |
| Published online | 08 January 2018 | |
Validation of positive expectation dependence
1 AGH University of Science and Technology, Faculty of Applied Mathematics, Al. Mickiewicza 30, 30-059 Cracow, Poland .
cmielbog@gmail.com
2 Polish Academy of Sciences, Institute of Mathematics, ul. Kopernika 18, 51-617 Wrocław, Poland.
ledwina@impan.pl
Received: 9 January 2017
Revised: 12 July 2017
Accepted: 3 August 2017
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.
Mathematics Subject Classification: 60F05 / 62G09 / 62G10 / 62G20
Key words: Hypothesis testing / expectation dependence / Lorenz curve / monotonic dependence function / multiplier central limit theorem / wild bootstrap / Zenga curve
© EDP Sciences, SMAI, 2017
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