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A note on minimum distance estimation of copula densities

Author

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  • Biau, Gérard
  • Wegkamp, Marten

Abstract

This paper introduces a minimum L1 distance estimate for parametric copula densities. It is shown that the expected L1 error of the estimate is within a given constant multiple of the best possible error plus an additive remainder term which is small under mild assumptions. The proof is based on an oracle inequality and a maximal inequality for the empirical copula process indexed by sets.

Suggested Citation

  • Biau, Gérard & Wegkamp, Marten, 2005. "A note on minimum distance estimation of copula densities," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 105-114, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:2:p:105-114
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    References listed on IDEAS

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    1. Biau, Gérard & Devroye, Luc, 2005. "Density estimation by the penalized combinatorial method," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 196-208, May.
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    Cited by:

    1. Kallenberg, Wilbert C.M., 2008. "Modelling dependence," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 127-146, February.
    2. Robert M. Mnatsakanov & Hansjoerg Albrecher & Stephane Loisel, 2022. "Approximations of Copulas via Transformed Moments," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3175-3193, December.
    3. Mohamed Belalia & Jean-François Quessy, 2024. "Generalized simulated method-of-moments estimators for multivariate copulas," Statistical Papers, Springer, vol. 65(8), pages 4811-4841, October.
    4. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, vol. 6(4), pages 511-535, October.
    5. O. Chatrabgoun & G. Parham & R. Chinipardaz, 2017. "A Legendre multiwavelets approach to copula density estimation," Statistical Papers, Springer, vol. 58(3), pages 673-690, September.
    6. Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
    7. Kallenberg, Wilbert C.M., 2009. "Estimating copula densities, using model selection techniques," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 209-223, October.

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