Bernoulli

  • Bernoulli
  • Volume 19, Number 5A (2013), 1655-1687.

Multiplier bootstrap of tail copulas with applications

Axel Bücher and Holger Dette

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Abstract

For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the empirical tail copula process and requires estimation of the partial derivatives of the tail copula. The second method avoids this estimation problem and uses multipliers in the two-dimensional empirical distribution function and in the estimates of the marginal distributions. For both multiplier bootstrap procedures, we prove consistency.

For these investigations, we demonstrate that the common assumption of the existence of continuous partial derivatives in the the literature on tail copula estimation is so restrictive, such that the tail copula corresponding to tail independence is the only tail copula with this property. Moreover, we are able to solve this problem and prove weak convergence of the empirical tail copula process under nonrestrictive smoothness assumptions that are satisfied for many commonly used models. These results are applied in several statistical problems, including minimum distance estimation and goodness-of-fit testing.

Article information

Source
Bernoulli, Volume 19, Number 5A (2013), 1655-1687.

Dates
First available in Project Euclid: 5 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1383661198

Digital Object Identifier
doi:10.3150/12-BEJ425

Mathematical Reviews number (MathSciNet)
MR3129029

Zentralblatt MATH identifier
1281.62124

Keywords
comparison of tail copulas goodness-of-fit minimum distance estimation multiplier bootstrap stable tail dependence function tail copula

Citation

Bücher, Axel; Dette, Holger. Multiplier bootstrap of tail copulas with applications. Bernoulli 19 (2013), no. 5A, 1655--1687. doi:10.3150/12-BEJ425. https://projecteuclid.org/euclid.bj/1383661198


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