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Chuan-Fa Tang1, Dewei Wang2, Hammou El Barmi3

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Summary
This summary is machine-generated.

This study introduces a new statistical test for positive quadrant dependence (PQD) between two variables X and Y. The empirical likelihood method offers a robust way to detect this dependence in various fields.

Keywords:
Bivariate dataCopula functionEmpirical likelihoodIndependenceKendall’s rank testSpearman’s rank test

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Testing independence of random variables is crucial in applied statistics.
  • Positive Quadrant Dependence (PQD) describes a specific type of positive association between variables, important in finance, insurance, and engineering.
  • Existing methods for detecting PQD have limitations.

Purpose of the Study:

  • To develop a novel distribution-free statistical test for positive quadrant dependence (PQD).
  • To assess the performance of the proposed test against existing methods.
  • To provide a practical tool for implementing the test in real-world applications.

Main Methods:

  • An empirical likelihood (EL) approach is developed to test independence against the alternative of strict PQD.
  • A distribution-free test statistic is constructed by integrating a localized empirical likelihood ratio.
  • The method is compared with existing tests and copula-based distance tests through simulations.

Main Results:

  • The proposed EL testing procedure demonstrates strong performance in detecting strict PQD across various scenarios.
  • Simulation results indicate the EL test is competitive with and often superior to existing methods.
  • The study provides an accessible online R resource for practitioners.

Conclusions:

  • The empirical likelihood approach provides an effective and robust method for testing positive quadrant dependence.
  • The developed test is suitable for practical applications in fields requiring analysis of positive association between variables.
  • The availability of an R package facilitates the adoption of this statistical methodology.