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On the estimation of the characteristic function in finite populations with applications

Author

Listed:
  • M. D. Jiménez-Gamero

    (Universidad de Sevilla)

  • J. L. Moreno-Rebollo

    (Universidad de Sevilla)

  • J. A. Mayor-Gallego

    (Universidad de Sevilla)

Abstract

This paper studies the estimation of the characteristic function of a finite population. Specifically, the weak convergence of the finite population empirical characteristic process is studied. Under suitable assumptions, it has the same limit as the empirical characteristic process for independent, identically distributed data from a random variable, up to a multiplicative constant depending on the sampling design. Applications of the obtained results for the two-sample problem, testing for independence and testing for symmetry are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0514-2
    DOI: 10.1007/s11749-016-0514-2
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    References listed on IDEAS

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    1. 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.
    2. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    3. Henze, N. & Klar, B. & Zhu, L. X., 2005. "Checking the adequacy of the multivariate semiparametric location shift model," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 238-256, April.
    4. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    5. 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.
    6. Pier Luigi Conti & Daniela Marella, 2015. "Inference for Quantiles of a Finite Population: Asymptotic versus Resampling Results," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 545-561, June.
    7. Wang, Jianqiang C., 2012. "Sample distribution function based goodness-of-fit test for complex surveys," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 664-679.
    8. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    9. Xiao, Yuanhui, 2017. "A fast algorithm for two-dimensional Kolmogorov–Smirnov two sample tests," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 53-58.
    10. Hlávka, Zdenek & Husková, Marie & Meintanis, Simos G., 2011. "Tests for independence in non-parametric heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 816-827, April.
    11. 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.
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    Cited by:

    1. Daniela Marella & Paola Vicard, 2022. "Bayesian network structural learning from complex survey data: a resampling based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 981-1013, October.
    2. S. G. Meintanis & M. Hušková & M. D. Jiménez-Gamero, 2018. "Editorial," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-2, March.

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