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Superefficient estimation of the marginals by exploiting knowledge on the copula

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  • Einmahl, John H.J.
  • van den Akker, Ramon

Abstract

We consider the problem of estimating the marginals in the case where there is knowledge on the copula. If the copula is smooth, it is known that it is possible to improve on the empirical distribution functions: optimal estimators still have a rate of convergence n-1/2, but a smaller asymptotic variance. In this paper we show that for non-smooth copulas it is sometimes possible to construct superefficient estimators of the marginals: we construct both a copula and, exploiting the information our copula provides, estimators of the marginals with the rate of convergence logn/n.

Suggested Citation

  • Einmahl, John H.J. & van den Akker, Ramon, 2011. "Superefficient estimation of the marginals by exploiting knowledge on the copula," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1315-1319, October.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1315-1319
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    References listed on IDEAS

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    1. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
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    Keywords

    Copula Estimation of marginals Superefficient estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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