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Nonparametric probability weighted empirical characteristic function and applications

Author

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  • Meintanis, Simos G.
  • Ushakov, Nikolai G.

Abstract

We study certain properties of probability weighted quantities and suggest a nonparametric estimator of the probability weighted characteristic function introduced by Meintanis et al. (2014). Some properties of this estimator are studied and corresponding inference procedures for symmetry and the two-sample problem are proposed. Monte Carlo results on the finite-sample behavior of the procedures are also included.

Suggested Citation

  • Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    • Handle: RePEc:eee:stapro:v:108:y:2016:i:c:p:52-61
    DOI: 10.1016/j.spl.2015.08.021
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    References listed on IDEAS

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    1. Alba Fernández, V. & Jiménez Gamero, M.D. & Muñoz Garcia, J., 2008. "A test for the two-sample problem based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3730-3748, March.
    2. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    3. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    4. Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
    5. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    6. Quessy, Jean-François & Éthier, François, 2012. "Cramér–von Mises and characteristic function tests for the two and k-sample problems with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2097-2111.
    7. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    8. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    9. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    10. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    11. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    12. T.W. Epps, 2005. "Tests for location-scale families based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 99-114, September.
    13. Marie Hušková & Simos Meintanis, 2006. "Change Point Analysis based on Empirical Characteristic Functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 145-168, April.
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    Cited by:

    1. Nowak, Piotr Bolesław, 2019. "Moment-type estimation from grouped samples," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 80-85.
    2. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    3. Simos G. Meintanis & James Allison & Leonard Santana, 2016. "Goodness-of-fit tests for semiparametric and parametric hypotheses based on the probability weighted empirical characteristic function," Statistical Papers, Springer, vol. 57(4), pages 957-976, December.

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