A note on bootstrap approximations for the empirical copula process

Bücher, Axel; Dette, Holger

doi:10.1016/j.spl.2010.08.021

Cited by 59 publications

(61 citation statements)

References 14 publications

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“…, ξ n,n satisfies assumptions (M1), (M2) and (M3). From a practical perspective, for the function ϕ, we considered the Bartlett and Parzen kernels κ B and κ P , as well as κ U,6 and κ U, 8 , where κ U,p is the density function of the sum of p independent uniforms centered at 0, normalized so that it equals 1 at 0, and rescaled to have support (−1, 1). The functions κ U,6 and κ U,8 are represented in Figure 1.…”

Section: The Covariance Matrix Approachmentioning

confidence: 99%

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

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Two key ingredients to carry out inference on the copula of multivariate observations are the empirical copula process and an appropriate resampling scheme for the latter. Among the existing techniques used for i.i.d. observations, the multiplier bootstrap of Rémillard and Scaillet (J. Multivariate Anal. 100 (2009) 377-386) frequently appears to lead to inference procedures with the best finite-sample properties. Bücher and Ruppert (J. Multivariate Anal. 116 (2013) 208-229) recently proposed an extension of this technique to strictly stationary strongly mixing observations by adapting the dependent multiplier bootstrap of Bühlmann (The blockwise bootstrap in time series and empirical processes (1993) ETH Zürich, Section 3.3) to the empirical copula process. The main contribution of this work is a generalization of the multiplier resampling scheme proposed by Bücher and Ruppert along two directions. First, the resampling scheme is now genuinely sequential, thereby allowing to transpose to the strongly mixing setting many of the existing multiplier tests on the unknown copula, including nonparametric tests for change-point detection. Second, the resampling scheme is now fully automatic as a data-adaptive procedure is proposed which can be used to estimate the bandwidth parameter. A simulation study is used to investigate the finite-sample performance of the resampling scheme and provides suggestions on how to choose several additional parameters. As by-products of this work, the validity of a sequential version of the dependent multiplier bootstrap for empirical processes of Bühlmann is obtained under weaker conditions on the strong mixing coefficients and the multipliers, and the weak convergence of the sequential empirical copula process is established under many serial dependence conditions. Keywords: lag window estimator; multiplier central limit theorem; multivariate observations; partial-sum process; ranks; serial dependence This is an electronic reprint of the original article published by the ISI/BS in Bernoulli, 2016, Vol. 22, No. 2, 927-968. This reprint differs from the original in pagination and typographic detail.

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Section: The Covariance Matrix Approachmentioning

confidence: 99%

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

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“…Theorem 1.12.4 in Van der Vaart and Wellner (1996). The process B C can be approximated by multiplier bootstrap methods, see Bücher (2011);Bücher and Dette (2010); Rémillard and Scaillet (2009);Segers (2011). More precisely, let ξ 1 , .…”

Section: A Multiplier Bootstrap Approximationmentioning

confidence: 99%

A test for Archimedeanity in bivariate copula models

Bücher

Dette

Volgushev

2012

Journal of Multivariate Analysis

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We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-upper bound. We prove weak convergence of this statistic and show that the critical values of the corresponding test can be determined by the multiplier bootstrap method. The test is shown to be consistent against all departures from Archimedeanity if the copula satisfies weak smoothness assumptions. A simulation study is presented which illustrates the finite sample properties of the new test.

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“…Some precedent studies have used the bootstrap method to approximate the limiting distribution. Bücher and Dette [25] compared the finite sample properties of the various bootstrap methods proposed in the literature and concluded that the procedure proposed by Rémillard and Scaillet [24] yields the best results in most cases. In this study, we consider the multiplier bootstrap approach proposed by Rémillard and Scaillet [24].…”

Section: Lemmamentioning

confidence: 99%

“…To overcome this problem, several authors have suggested bootstrap methods for approximating the Kiefer process. We refer to Fermanian et al [23], Rémillard and Scaillet [24], Bücher and Dette [25], Bouzebda [26] and the references therein for more details. In this study, we also utilize the bootstrap method to deal with this difficulty.…”

Section: Introductionmentioning

confidence: 99%

Monitoring Test for Stability of Dependence Structure in Multivariate Data Based on Copula

Kim

2016

Entropy

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Abstract:In this paper, we consider a sequential monitoring procedure for detecting changes in copula function. We propose a cusum type of monitoring test based on the empirical copula function and apply it to the detection of the distributional changes in copula function. We investigate the asymptotic properties of the stopping time and show that under regularity conditions, its limiting null distribution is the same as the sup of Kiefer process. Moreover, we utilize the bootstrap method in order to obtain the limiting distribution. A simulation study and a real data analysis are conducted to evaluate our test.

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A note on bootstrap approximations for the empirical copula process

Cited by 59 publications

References 14 publications

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

A test for Archimedeanity in bivariate copula models

Monitoring Test for Stability of Dependence Structure in Multivariate Data Based on Copula

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