Superefficient estimation of the marginals by exploiting knowledge on the copula

Research output: Contribution to journalArticleScientificpeer-review

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 log n/n.
Original languageEnglish
Pages (from-to)1315-1319
JournalJournal of Multivariate Analysis
Volume102
Issue number9
DOIs
Publication statusPublished - 2011

Fingerprint

Copula
Distribution functions
Estimator
Rate of Convergence
Empirical Distribution Function
Asymptotic Variance
Knowledge
Rate of convergence

Cite this

@article{48925104b15d48bb8965b821a8d36bc3,
title = "Superefficient estimation of the marginals by exploiting knowledge on the copula",
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 log n/n.",
author = "J.H.J. Einmahl and {van den Akker}, R.",
note = "Appeared earlier as CentER Discussion Paper 2010-120",
year = "2011",
doi = "10.1016/j.jmva.2011.04.015",
language = "English",
volume = "102",
pages = "1315--1319",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",
number = "9",

}

Superefficient estimation of the marginals by exploiting knowledge on the copula. / Einmahl, J.H.J.; van den Akker, R.

In: Journal of Multivariate Analysis, Vol. 102, No. 9, 2011, p. 1315-1319.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Superefficient estimation of the marginals by exploiting knowledge on the copula

AU - Einmahl, J.H.J.

AU - van den Akker, R.

N1 - Appeared earlier as CentER Discussion Paper 2010-120

PY - 2011

Y1 - 2011

N2 - 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 log n/n.

AB - 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 log n/n.

U2 - 10.1016/j.jmva.2011.04.015

DO - 10.1016/j.jmva.2011.04.015

M3 - Article

VL - 102

SP - 1315

EP - 1319

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 9

ER -