Integer-Valued Time Series

Akker, R. van den

doi:10.2139/ssrn.2412998

Cited by 4 publications

(1 citation statement)

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“…[3] also noted that exploiting the knowledge on the copula may help to improve on the marginal empirical distribution functions. Following the setup in [3], [1] and [7,Chapter 5] provide efficient estimators of the marginals, incorporating the information the copula provides, with the standard rate of convergence n −1/2 and a limiting distribution that has less spread than the limiting distribution of the empirical distribution functions.…”

Section: Introductionmentioning

confidence: 99%

Superefficient estimation of the marginals by exploiting knowledge on the copula

Einmahl¹,

Akker²

2011

Journal of Multivariate Analysis

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a b s t r a c tWe 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.

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