Abstract
This paper uses independence-type characterizations to propose a class of test statistics which can be used for testing goodness-of-fit with several classes of null distributions. The resulting tests are consistent against fixed alternatives. Some limiting and small sample properties of the test statistics are explored. In comparison with common universal goodness-of-fit tests, the new tests exhibit better power for most of the alternatives considered, while in comparison with another characterization-based procedure, the new tests provide competitive or comparable power in various simulation settings. The handiness of the proposed tests is demonstrated through several real-data examples.
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Acknowledgements
We thank the associate editor and two anonymous referees for their useful remarks that improved the quality of the paper.
Funding
The work of K. Halaj and B. Milošević has been supported by the Ministry of Science, Technological Development and Innovations of the Republic of Serbia (contracts 451-03-47/2023-01/ 200128 and 451-03-47/2023-01/ 200104, respectively). The work of B. Milošević is also supported by the COST action CA21163 - Text, functional and other high-dimensional data in econometrics: New models, methods, applications (HiTEc). M.D. Jiménez-Gamero has been partially supported by Grants PID2020-118101GB-I00 (Ministerio de Ciencia e Innovación, MCIN/AEI/10.13039/501100011033), P18-FR-2269 (Junta de Andalucía) and US-1381178 (Junta de Andalucía).
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Halaj, K., Milošević, B., Obradović, M. et al. Correlation-type goodness-of-fit tests based on independence characterizations. AStA Adv Stat Anal 108, 185–207 (2024). https://doi.org/10.1007/s10182-023-00475-x
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DOI: https://doi.org/10.1007/s10182-023-00475-x