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Validation of association

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  • Ćmiel, Bogdan
  • Ledwina, Teresa

Abstract

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests for independence and to provide an easily interpretable diagnostic plot of existing departures from the null model. The dependence function is designed to detect general dependence structure between variables in quantiles of the joint distribution. It gives an insight into how the dependence structure changes in different parts of the joint distribution. We define new estimators of the dependence function, discuss some of their properties, and apply them to construct new tests of independence. Numerical evidence is given to the tests benefits against three recognized independence tests introduced in the previous years. In real-data analysis, we offer the use of our tests and the graphical presentation of the underlying dependence structure.

Suggested Citation

  • Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:55-67
    DOI: 10.1016/j.insmatheco.2019.12.003
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    References listed on IDEAS

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    Cited by:

    1. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.

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    More about this item

    Keywords

    Copula; Cross-quantilogram; Independence testing; Measure of dependence; Quantile dependence function; Weighted statistics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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