Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula

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Abstract

We consider the problem of estimating the marginals in case 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 rate of convergence n−1/2, but a smaller asymptotic variance. In this paper we show that smoothness assumptions on the copula are necessary: we construct both a (non-smooth) copula and, exploiting the information our copula provides, estimators of the marginals with rate of convergence log n/n.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages8
Volume2010-120
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-120

Fingerprint

Copula
Rate of Convergence
Estimator
Empirical Distribution Function
Asymptotic Variance
Smoothness
Knowledge
Necessary

Keywords

  • copula
  • estimation of marginals
  • superefficient estimation

Cite this

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title = "Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula",
abstract = "We consider the problem of estimating the marginals in case 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 rate of convergence n−1/2, but a smaller asymptotic variance. In this paper we show that smoothness assumptions on the copula are necessary: we construct both a (non-smooth) copula and, exploiting the information our copula provides, estimators of the marginals with rate of convergence log n/n.",
keywords = "copula, estimation of marginals, superefficient estimation",
author = "J.H.J. Einmahl and {van den Akker}, R.",
note = "Subsequently published in the Journal of Multivariate Analysis (2011) Pagination: 8",
year = "2010",
language = "English",
volume = "2010-120",
series = "CentER Discussion Paper",
publisher = "Econometrics",
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Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula. / Einmahl, J.H.J.; van den Akker, R.

Tilburg : Econometrics, 2010. (CentER Discussion Paper; Vol. 2010-120).

Research output: Working paperDiscussion paperOther research output

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T1 - Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula

AU - Einmahl, J.H.J.

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N2 - We consider the problem of estimating the marginals in case 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 rate of convergence n−1/2, but a smaller asymptotic variance. In this paper we show that smoothness assumptions on the copula are necessary: we construct both a (non-smooth) copula and, exploiting the information our copula provides, estimators of the marginals with rate of convergence log n/n.

AB - We consider the problem of estimating the marginals in case 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 rate of convergence n−1/2, but a smaller asymptotic variance. In this paper we show that smoothness assumptions on the copula are necessary: we construct both a (non-smooth) copula and, exploiting the information our copula provides, estimators of the marginals with rate of convergence log n/n.

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KW - estimation of marginals

KW - superefficient estimation

M3 - Discussion paper

VL - 2010-120

T3 - CentER Discussion Paper

BT - Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula

PB - Econometrics

CY - Tilburg

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