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Goodness-of-fit tests for semiparametric and parametric hypotheses based on the probability weighted empirical characteristic function

Author

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  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North-West University)

  • James Allison

    (North-West University)

  • Leonard Santana

    (North-West University)

Abstract

We investigate the finite-sample properties of certain procedures which employ the novel notion of the probability weighted empirical characteristic function. The procedures considered are: (1) Testing for symmetry in regression, (2) Testing for multivariate normality with independent observations, and (3) Testing for multivariate normality of random effects in mixed models. Along with the new tests alternative methods based on the ordinary empirical characteristic function as well as other more well known procedures are implemented for the purpose of comparison.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0760-0
    DOI: 10.1007/s00362-016-0760-0
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    References listed on IDEAS

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    1. 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.
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    3. Frederico Caeiro & M. Ivette Gomes & Björn Vandewalle, 2014. "Semi-Parametric Probability-Weighted Moments Estimation Revisited," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 1-29, March.
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    7. 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.
    8. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    9. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    10. Simos G. Meintanis & Gilles Stupfler, 2015. "Transformations to symmetry based on the probability weighted characteristic function," Post-Print hal-01457397, HAL.
    11. Simos G. Meintanis & James S. Allison & Leonard Santana, 2016. "Diagnostic tests for the distribution of random effects in multivariate mixed effects models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 201-215, January.
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    Cited by:

    1. Zhihua Sun & Dongshan Luo & Xiaohua Zhou & Qingzhao Zhang, 2021. "Comparative studies on the adequacy check of parametric measurement error models with auxiliary variable," Statistical Papers, Springer, vol. 62(4), pages 1723-1751, August.
    2. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
    3. Ingo Hoffmann & Christoph J. Börner, 2021. "The risk function of the goodness-of-fit tests for tail models," Statistical Papers, Springer, vol. 62(4), pages 1853-1869, August.
    4. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    5. Marie Hušková & Simos G. Meintanis & Charl Pretorius, 2022. "Tests for heteroskedasticity in transformation models," Statistical Papers, Springer, vol. 63(4), pages 1013-1049, August.
    6. Ivanović, Blagoje & Milošević, Bojana & Obradović, Marko, 2020. "Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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