Tests for symmetry based on the integrated empirical process

References

• Ahmad, I. A., and Q. Li. 1997. Testing symmetry of an unknown density function by kernel method. Journal of Nonparametric Statistics 7 (3):279–93. doi:10.1080/10485259708832704.
   Google Scholar
• Allison, J. S., and C. Pretorius. 2017. A Monte Carlo evaluation of the performance of two new tests for symmetry. Computational Statistics 32 (4):1323–38. doi:10.1007/s00180-016-0680-4.
   Web of Science ®Google Scholar
• Antille, A., G. Kersting, and W. Zucchini. 1982. Testing symmetry. Journal of the American Statistical Association 77 (379):639–46. doi:10.1080/01621459.1982.10477863.
   Web of Science ®Google Scholar
• Betsch, S., and B. Ebner. 2021. Fixed point characterizations of continuous univariate probability distributions and their applications. Annals of the Institute of Statistical Mathematics 73 (1):31–59. doi:10.1007/s10463-019-00735-1.
   Web of Science ®Google Scholar
• Bickel, P. J. 1982. On adaptive estimation. The Annals of Statistics 10 (3):647–71. doi:10.1214/aos/1176345863.
   Web of Science ®Google Scholar
• Billingsley, P. 1968. Convergence of probability measures. New York: John Wiley & Sons.
   Google Scholar
• Boos, D. D. 1982. A test for asymmetry associated with the Hodges–Lehmann estimator. Journal of the American Statistical Association 77 (379):647–51. doi:10.1080/01621459.1982.10477864.
   Web of Science ®Google Scholar
• Božin, V., B. Milošević, Y. Y. Nikitin, and M. Obradović. 2020. New characterization-based symmetry tests. Bulletin of the Malaysian Mathematical Sciences Society 43 (1):297–320. doi:10.1007/s40840-018-0680-3.
   Web of Science ®Google Scholar
• Cabilio, P., and J. Masaro. 1996. A simple test of symmetry about an unknown median. Canadian Journal of Statistics 24 (3):349–61. doi:10.2307/3315744.
   Web of Science ®Google Scholar
• Chen, F., S. G. Meintanis, and L. Zhu. 2019. On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence. Journal of Multivariate Analysis 173:125–44. doi:10.1016/j.jmva.2019.02.006.
   Web of Science ®Google Scholar
• Davis, C. E., and D. Quade. 1978. U-statistics for skewness or symmetry. Communications in Statistics – Theory and Methods 7 (5):413–8. doi:10.1080/03610927808827634.
   Web of Science ®Google Scholar
• Ebner, B., and S. C. Liebenberg. 2021. On a new test of fit to the beta distribution. Stat 10 (1):e341. doi:10.1002/sta4.341.
   Web of Science ®Google Scholar
• Fan, Y., and R. Gencay. 1995. A consistent nonparametric test of symmetry in linear regression models. Journal of the American Statistical Association 90 (430):551–7. doi:10.1080/01621459.1995.10476547.
   Web of Science ®Google Scholar
• Feuerverger, A., and R. A. Mureika. 1977. The empirical characteristic function and its applications. The Annals of Statistics 5 (1):88–97. doi:10.1214/aos/1176343742.
   Web of Science ®Google Scholar
• Ghosh, S., and F. H. Ruymgaart. 1992. Applications of empirical characteristic functions in some multivariate problems. Canadian Journal of Statistics 20 (4):429–40. doi:10.2307/3315612.
   Web of Science ®Google Scholar
• Gupta, M. K. 1967. An asymptotically nonparametric test of symmetry. The Annals of Mathematical Statistics 38 (3):849–66. doi:10.1214/aoms/1177698879.
   Google Scholar
• Henze, N., and Y. Y. Nikitin. 2000. A new approach to goodness-of-fit testing based on the integrated empirical process. Journal of Nonparametric Statistics 12 (3):391–416. doi:10.1080/10485250008832815.
   Web of Science ®Google Scholar
• Henze, N., B. Klar, and S. G. Meintanis. 2003. Invariant tests for symmetry about an unspecified point based on the empirical characteristic function. Journal of Multivariate Analysis 87 (2):275–97. doi:10.1016/S0047-259X(03)00044-7.
   Web of Science ®Google Scholar
• Hušková, M., and S. G. Meintanis. 2007. Omnibus tests for the error distribution in the linear regression model. Statistics 41 (5):363–76. doi:10.1080/02331880701442643.
   Web of Science ®Google Scholar
• Hušková, M., and S. G. Meintanis. 2012. Tests for symmetric error distribution in linear and nonparametric regression models. Communications in Statistics – Simulation and Computation 41 (6):833–51. doi:10.1080/03610918.2012.625330.
   Web of Science ®Google Scholar
• Ivanović, B., B. Milošević, and M. Obradović. 2020. Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting. Computational Statistics & Data Analysis 151:106991. doi:10.1016/j.csda.2020.106991.
   Web of Science ®Google Scholar
• Klar, B. 2001. Goodness-of-fit tests for the exponential and the normal distribution based on the integrated distribution function. Annals of the Institute of Statistical Mathematics 53 (2):338–53. doi:10.1023/A:1012422823063.
   Web of Science ®Google Scholar
• Koul, H. L. 2002. Weighted empirical processes in dynamic nonlinear models. 2nd ed. New York: Springer.
   Google Scholar
• Koutrouvelis, I. A. 1985. Distribution-free procedures for location and symmetry inference problems based on the empirical characteristic function. Scandinavian Journal of Statistics 12:257–69.
   Web of Science ®Google Scholar
• Malan, R. D. 2017. An evaluation of various tests for symmetry. Master’s thesis., North-West University, Potchefstroom.
   Google Scholar
• Miloševic, B. 2017. Some recent characterization based goodness of fit tests. In The Proceedings of the 20th European Young Statisticians Meeting, 67–73.
   Google Scholar
• Milošević, B., and M. Obradović. 2016. Characterization based symmetry tests and their asymptotic efficiencies. Statistics & Probability Letters 119:155–62. doi:10.1016/j.spl.2016.07.007.
   Web of Science ®Google Scholar
• Muliere, P., and Y. Y. Nikitin. 2002. Scaleinvariant test of normality based on Polya’s characterization. Metron 60 (1–2):21–33.
   Google Scholar
• National Institute of Standards and Technology. 2012. NIST/SEMATECH e-Handbook of statistical methods.
   Google Scholar
• Neumeyer, N., H. Dette, and E. R. Nagel. 2005. A note on testing symmetry of the error distribution in linear regression models. Journal of Nonparametric Statistics 17 (6):697–715. doi:10.1080/10485250500095660.
   Web of Science ®Google Scholar
• Newey, W. K., and D. G. Steigerwald. 1997. Asymptotic bias for quasi-maximum-likelihood estimators in conditional heteroskedasticity models. Econometrica 65 (3):587–99. doi:10.2307/2171754.
   Web of Science ®Google Scholar
• Nikitin, Y. Y. 2017. Tests based on characterizations, and their efficiencies: A survey. Acta et Commentationes Universitatis Tartuensis de Mathematica 21 (1):3–24. doi:10.12697/ACUTM.2017.21.01.
   Google Scholar
• Nikitin, Y. Y., and K. Y. Volkova. 2016. Efficiency of exponentiality tests based on a special property of exponential distribution. Mathematical Methods of Statistics 25 (1):54–66. doi:10.3103/S1066530716010038.
   Web of Science ®Google Scholar
• Petrov, V. V. 1995. Limit theorems of probability theory: Sequences of independent random variables. Oxford, UK: Oxford University Press.
   Google Scholar
• Randles, R. H., M. A. Fligner, G. E. Policello, and D. A. Wolfe. 1980. An asymptotically distribution-free test for symmetry versus asymmetry. Journal of the American Statistical Association 75 (369):168–72. doi:10.1080/01621459.1980.10477448.
   Web of Science ®Google Scholar
• Rothman, E. D., and M. Woodroofe. 1972. A Cramér–von Mises type statistic for testing symmetry. The Annals of Mathematical Statistics 43 (6):2035–8. doi:10.1214/aoms/1177690879.
   Google Scholar
• Silver, E. A., and D. Costa. 1997. A property of symmetric distributions and a related order statistic result. The American Statistician 51 (1):32–3. doi:10.2307/2684689.
   Web of Science ®Google Scholar
• Tenreiro, C. 2009. On the choice of the smoothing parameter for the BHEP goodness-of-fit test. Computational Statistics & Data Analysis 53 (4):1038–53. doi:10.1016/j.csda.2008.09.002.
   Web of Science ®Google Scholar
• Tenreiro, C. 2019. On the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests. Journal of Statistical Computation and Simulation 89 (10):1780–97. doi:10.1080/00949655.2019.1598409.
   Web of Science ®Google Scholar
• Zardasht, V. 2018. A bootstrap test for symmetry based on quantiles. Hacettepe Journal of Mathematics and Statistics 47:1061–9.
   Web of Science ®Google Scholar