K-sample problem using strong approximations of empirical copula processes

Bouzebda, Salim; Keziou, Amor; Zari, Tarek

doi:10.3103/s1066530711010029

Cited by 16 publications

(13 citation statements)

References 16 publications

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“…That is why it will be discussed hereafter. Note that the 2-sample copula problem has already been addressed by [35], and the msample by [10]. However, both paper are designed only in a nonparametric framework, and these authors have not noticed the connection with the simplifying assumption.…”

Section: Example 2 To Illustrate the Problem Let Us Consider A Simpmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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Abstract:We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non-and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.

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Section: Example 2 To Illustrate the Problem Let Us Consider A Simpmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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“…Rémillard and Scaillet (2009) propose a test of equality between two copulas, but we need a test for a general number of groups m. Bouzebda et al (2011) develop mathematical results for the m-sample empirical copula process, but while their results could lead to tests of equality for m samples, we could not locate a numerical implementation of such tests nor any results showing their finite sample properties. In the case study, we rather use resampling techniques to test the homogeneity of the copulas.…”

Section: Remarkmentioning

confidence: 99%

“…As mentioned in Section 3.1, Rémillard and Scaillet (2009) have developped a solution for m = 2 and the results from Bouzebda et al (2011) for more groups have not been implemented numerically nor tested on finite samples. While further developments of such tests will certainly offer better options in the near future, we choose here to use a resampling method that we present next.…”

Section: Resampling Technique For Testing the Homogeneity Of Copulasmentioning

confidence: 99%

Rank correlation under categorical confounding

Plante

2017

J Stat Distrib App

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Rank correlation is invariant to bijective marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation for continuous variables developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

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“…For the extension to the multivariate framework, we may refer to Jing and Wang (2006) and Jing and Yang (2007) where some projected integrated empirical processes for testing the equality of two multivariate distributions are considered. Inspired by the work of Henze and Nikitin (2003), Bouzebda and El Faouzi (2012) developed multivariate twosample testing procedures based on the integrated empirical copula process that are extended to the K-sample problem in Bouzebda et al (2011). Emphasis is placed on the explanation of the strong approximation methodology.…”

Section: Introductionmentioning

confidence: 99%

Strong approximations for the p-fold integrated empirical process with applications to statistical tests

Alvarez-Andrade

Bouzebda

Lachal

2017

TEST

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The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process, p being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. We obtain an exponential bound for the tail probability of the weighted approximation to the p-fold integrated empirical process. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of integrated empirical processes when the parameters are estimated. We study the behavior of the self-intersection local time of the partial sum process representation of integrated empirical processes. Finally, simulation results are provided to illustrate the finite sample performance of the proposed statistical tests based on the integrated empirical processes.

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K-sample problem using strong approximations of empirical copula processes

Cited by 16 publications

References 16 publications

About tests of the “simplifying” assumption for conditional copulas

About tests of the “simplifying” assumption for conditional copulas

Rank correlation under categorical confounding

Strong approximations for the p-fold integrated empirical process with applications to statistical tests

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