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Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function

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  • Fan, Yanqin
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    Abstract

    In this paper, we take the characteristic function approach to goodness-of-fit tests. It has several advantages over existing methods: First, unlike the popular comparison density function approach suggested in Parzen (1979), our approach is applicable to both univariate and multivariate data; Second, in the case where the null hypothesis is composite, the approach taken in this paper yields a test that is superior to tests based on empirical distribution functions such as the Cramér- von Mises test, because on the one hand the asymptotic critical values of our test are easily obtained from the standard normal distribution and are not affected by-consistent estimation of the unknown parameters in the null hypothesis, and on the other hand, our test extends that in Eubank and LaRiccia (1992) and hence is more powerful than the Cramér-von Mises test for high-frequency alternatives.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 62 (1997)
    Issue (Month): 1 (July)
    Pages: 36-63

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    Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:36-63

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    Related research

    Keywords: characetistic function comparison density function the Cramer-von Mises test Fourier series consistent tests directional tests;

    References

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    1. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika, Springer, Springer, vol. 35(1), pages 339-348, December.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:
    1. Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 98(3), pages 533-543, March.
    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, Elsevier, vol. 53(12), pages 3957-3971, October.
    3. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, Elsevier, vol. 110(1), pages 1-26, September.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, Princeton University Press, edition 1, volume 1, number 8355.
    5. Lin, Liang-Ching & Lee, Sangyeol & Guo, Meihui, 2013. "Goodness-of-fit test for stochastic volatility models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 116(C), pages 473-498.
    6. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, Elsevier, vol. 164(2), pages 268-293, October.

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