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Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters

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  • Scaillet, Olivier

Abstract

We study a test statistic based on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U-statistic of order 4 with degeneracy of order 1. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular, size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.

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Bibliographic Info

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

Volume (Year): 98 (2007)
Issue (Month): 3 (March)
Pages: 533-543

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Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:533-543

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Keywords: Nonparametric Copula density Goodness-of-fit test U-statistic;

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References

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  1. Fan, Yanqin, 1997. "Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 36-63, July.
  2. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  3. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
  4. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
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Citations

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Cited by:
  1. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
  2. Shi, Peng, 2012. "Multivariate longitudinal modeling of insurance company expenses," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 204-215.
  3. Genest, Christian & RĂ©millard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
  4. Kelly, Robert & McCarthy, Yvonne & McQuinn, Kieran, 2011. "Impairment and Negative Equity in the Irish Mortgage Market," Research Technical Papers 9/RT/11, Central Bank of Ireland.
  5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 442-447, September.
  6. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(1), pages 62-82, March.
  7. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 24(4), pages 100-130.
  8. Braekers, Roel & Van Keilegom, Ingrid, 2009. "Flexible modeling based on copulas in nonparametric median regression," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1270-1281, July.

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