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Goodness-of-fit tests for multivariate skewed distributions based on the characteristic function

Abstract

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a discrepancy measure involving the distance between empirical characteristic functions and thus avoid the need for employing corresponding population quantities which may be unknown or complicated to work with. The only requirements of our tests are that we should be able to draw samples from the distribution under test and possess a reasonable method of estimation of the unknown distributional parameters. Monte Carlo studies are conducted to investigate the performance of the test criteria in finite samples for several families of skewed distributions. Real-data examples are also included to illustrate our method.

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Acknowledgements

The authors thank the review team for the comments that improved the manuscript. This research was supported by the King Abdullah University of Science and Technology (KAUST). Simos Meintanis wishes to sincerely thank Marc Genton and the staff of KAUST for the invitation and the hospitality rendered during his visit to KAUST.

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Correspondence to Maicon J. Karling.

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Simos G. Meintanis: On sabbatical leave from the University of Athens.

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Karling, M.J., Genton, M.G. & Meintanis, S.G. Goodness-of-fit tests for multivariate skewed distributions based on the characteristic function. Stat Comput 33, 99 (2023). https://doi.org/10.1007/s11222-023-10260-0

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