Geodesic
Validation of positive expectation dependence
Ćmiel, Bogdan1 ; Ledwina, Teresa2
1 AGH University of Science and Technology, Faculty of Applied Mathematics, Al. Mickiewicza 30, 30-059 Cracow, Poland
2 Polish Academy of Sciences, Institute of Mathematics, ul. Kopernika 18, 51-617 Wrocław, Poland.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 536-561

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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.

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DOI : 10.1051/ps/2017015
Classification : 60F05, 62G09, 62G10, 62G20
Keywords: Hypothesis testing, expectation dependence, Lorenz curve, monotonic dependence function, multiplier central limit theorem, wild bootstrap, Zenga curve

Ćmiel, Bogdan 1 ; Ledwina, Teresa 2

1 AGH University of Science and Technology, Faculty of Applied Mathematics, Al. Mickiewicza 30, 30-059 Cracow, Poland
2 Polish Academy of Sciences, Institute of Mathematics, ul. Kopernika 18, 51-617 Wrocław, Poland. 
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     author = {\'Cmiel, Bogdan and Ledwina, Teresa},
     title = {Validation of positive expectation dependence},
     journal = {ESAIM: Probability and Statistics},
     pages = {536--561},
     publisher = {EDP-Sciences},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2017015/}
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Ćmiel, Bogdan; Ledwina, Teresa. Validation of positive expectation dependence. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 536-561. doi: 10.1051/ps/2017015

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