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 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

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