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Goodness-of-fit tests based on empirical characteristic functions

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  • Jiménez-Gamero, M.D.
  • Alba-Fernández, V.
  • Muñoz-García, J.
  • Chalco-Cano, Y.

Abstract

A class of goodness-of-fit tests based on the empirical characteristic function is studied. They can be applied to continuous as well as to discrete or mixed data with any arbitrary fixed dimension. The tests are consistent against any fixed alternative for suitable choices of the weight function involved in the definition of the test statistic. The bootstrap can be employed to estimate consistently the null distribution of the test statistic. The goodness of the bootstrap approximation and the power of some tests in this class for finite sample sizes are investigated by simulation.

Suggested Citation

  • Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:3957-3971
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    References listed on IDEAS

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    1. M. D. Jiménez-Gamero & J. L. Moreno-Rebollo & J. A. Mayor-Gallego, 2018. "On the estimation of the characteristic function in finite populations with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 95-121, March.
    2. 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.
    3. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    4. Max Wornowizki & Roland Fried & Simos G. Meintanis, 2017. "Fourier methods for analyzing piecewise constant volatilities," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 289-308, July.
    5. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    6. Alba Fernández, M.V. & Jiménez Gamero, M.D. & Castillo Gutiérrez, S., 2014. "Approximating a class of goodness-of-fit test statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 24-38.
    7. Steffen Betsch & Bruno Ebner, 2021. "Fixed point characterizations of continuous univariate probability distributions and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 31-59, February.
    8. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    9. Bagkavos, Dimitrios & Patil, Prakash N. & Wood, Andrew T.A., 2023. "Nonparametric goodness-of-fit testing for a continuous multivariate parametric model," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    10. M. Dolores Jiménez-Gamero, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 893-897, December.
    11. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    12. 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.
    13. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.
    14. Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    15. Lin, Liang-Ching & Lee, Sangyeol & Guo, Meihui, 2013. "Goodness-of-fit test for stochastic volatility models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 473-498.
    16. Bahraoui Tarik & Bouezmarni Taoufik & Quessy Jean-François, 2018. "Testing the symmetry of a dependence structure with a characteristic function," Dependence Modeling, De Gruyter, vol. 6(1), pages 331-355, December.
    17. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2015. "An approximation to the null distribution of a class of Cramér–von Mises statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 258-272.

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