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Validation of positive quadrant dependence

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  • Ledwina, Teresa
  • Wyłupek, Grzegorz

Abstract

Quadrant dependence is a useful dependence notion of two random variables, widely applied in reliability, insurance and actuarial sciences. The interest in this dependence structure ranges from modeling it, throughout measuring its strength and investigations on how increasing the dependence effects of several reliability and economic indexes, to hypothesis testing on the dependence. In this paper, we focus on testing for positive quadrant dependence. We propose two new tests for verifying positive quadrant dependence. We prove novel results on finite sample behavior of power function of one of the proposed tests as well as evaluate and compare the two new solutions with the best existing ones, via a simulation study. These comparisons demonstrate that the new solutions are slightly weaker in detecting positive quadrant dependence modeled by classical bivariate models and outperform the best existing solutions when some mixtures, regression and heavy-tailed models have to be detected. Finally, the methods introduced in the paper are applied to real life insurance data, to assess the dependence and test them for positive quadrant dependence.

Suggested Citation

  • Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    • Handle: RePEc:eee:insuma:v:56:y:2014:i:c:p:38-47
    DOI: 10.1016/j.insmatheco.2014.02.008
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    References listed on IDEAS

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    Cited by:

    1. Zhao, Sihai Dave & Cai, T. Tony & Li, Hongzhe, 2017. "Optimal detection of weak positive latent dependence between two sequences of multiple tests," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 169-184.
    2. Guo, Xu & Li, Jingyuan, 2016. "Confidence band for expectation dependence with applications," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 141-149.
    3. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    4. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.

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    More about this item

    Keywords

    Concordance ordering; Copula; Correlation; Order preserving; Rank test;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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