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A Monte Carlo evaluation of the performance of two new tests for symmetry

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Abstract

We propose two new tests for symmetry based on well-known characterisations of symmetric distributions. The performance of the new tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. All tests are carried out in a regression setup where we test whether the error distribution in a linear regression model is symmetric. It is found that the newly proposed tests perform favourably compared to the other tests.

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Acknowledgments

The first author thanks the National Research Foundation of South Africa for financial support. The authors would also like to thank the referee and the associate editor for their constructive comments that led to an improvement of the paper.

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Authors and Affiliations

  1. Department of Statistics, North-West University, 1 Hoffman St, Potchefstroom, 2531, South Africa

    James S. Allison & Charl Pretorius

Authors
  1. James S. Allison
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  2. Charl Pretorius
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Correspondence to James S. Allison.

Appendix

Appendix

Table 9 contains the density (f) or distribution function (F) of the distributions considered in the Monte Carlo simulations.

Table 9 Density/distribution functions of the considered distributions
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Allison, J.S., Pretorius, C. A Monte Carlo evaluation of the performance of two new tests for symmetry. Comput Stat 32, 1323–1338 (2017). https://doi.org/10.1007/s00180-016-0680-4

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  • DOI: https://doi.org/10.1007/s00180-016-0680-4

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