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Fourier methods for model selection


  • M. D. Jiménez-Gamero

    (Universidad de Sevilla)

  • A. Batsidis

    (University of Ioannina)

  • M. V. Alba-Fernández

    () (Universidad de Jaén)


Abstract A test approach to the model selection problem based on characteristic functions (CFs) is proposed. The scheme is close to that proposed by Vuong (Econometrica 57:257–306, 1989), which is based on comparing estimates of the Kullback–Leibler distance between each candidate model and the true population. Other discrepancy measures could be used. This is specially appealing in cases where the likelihood of a model cannot be calculated or even, if it has a closed expression, it is either not easily tractable or not regular enough. In this work, the closeness is measured by means of a distance based on the CFs. As a prerequisite, some asymptotic properties of the minimum integrated squared error estimators are studied. From these properties, consistent tests for model selection based on CFs are given for separate, overlapping and nested models. Several examples illustrate the application of the proposed methods.

Suggested Citation

  • M. D. Jiménez-Gamero & A. Batsidis & M. V. Alba-Fernández, 2016. "Fourier methods for model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 105-133, February.
  • Handle: RePEc:spr:aistmt:v:68:y:2016:i:1:d:10.1007_s10463-014-0491-8
    DOI: 10.1007/s10463-014-0491-8

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    References listed on IDEAS

    1. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    2. 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.
    3. Muneya Matsui & Akimichi Takemura, 2008. "Goodness-of-fit tests for symmetric stable distributions—Empirical characteristic function approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 546-566, November.
    4. Muneya Matsui & Akimichi Takemura, 2005. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 183-199, March.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Jiménez-Gamero, M.D. & Pino-Mejías, R. & Alba-Fernández, V. & Moreno-Rebollo, J.L., 2011. "Minimum [phi]-divergence estimation in misspecified multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3365-3378, December.
    8. Hidetoshi Shimodaira, 1998. "An Application of Multiple Comparison Techniques to Model Selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 1-13, March.
    9. Vuong, Quang H. & Wang, Weiren, 1993. "Minimum chi-square estimation and tests for model selection," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 141-168, March.
    10. White, Halbert, 1982. "Regularity conditions for cox's test of non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 301-318, August.
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