Testing independence: count data case

ABSTRACT

This paper proposes several novel classes of independence tests specially designed for count data. The tests are based on the difference between joint and marginal probability generating functions and can be applied to count data of any arbitrary fixed dimension. The limiting properties of the test statistics are explored. The competitiveness of the novel proposal is demonstrated through an extensive empirical study, while the application is illustrated with a few real-data examples.

KEYWORDS:

• Empirical probability generating function
• weighted $L^p$ norm
• copula

Acknowledgments

The authors would like to express their gratitude to anonymous referees whose valuable suggestions have contributed significantly to improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 They are both increasing functions of the same standard uniform variable.

2 $Z_1$ is an increasing function and $Z_2$ a decreasing function of the same standard uniform variable.

Additional information

Funding

The work of B. Milošević is supported by the Ministry of Science, Technological Development and Innovations of the Republic of Serbia (451-03-66/2024-03/200104). In addition, the results of this paper are based upon her work from COST Action HiTEc-Text, functional and other high-dimensional data in econometrics: New models, methods, applications, CA21163, supported by COST (European Cooperation in Science and Technology).