Dependence structure of conditional Archimedean copulas

Mesfioui, Mhamed; Quessy, Jean‐François

doi:10.1016/j.jmva.2006.10.007

Cited by 21 publications

(14 citation statements)

References 15 publications

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“…The conditional copula (Mesfioui and Quessy, 2008) belongs to the Ali-Mikhail-Haq (AMH) family with dependence parameter γ(u 2 ; θ) = 1 − exp(−θu 2 ), i.e.,…”

Section: Example 2 (Trivariate Frank Copula)mentioning

confidence: 99%

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The partial copula: Properties and associated dependence measures

Spanhel

Kurz

2016

Statistics & Probability Letters

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“…The conditional copula (Mesfioui and Quessy, 2008) belongs to the Ali-Mikhail-Haq (AMH) family with dependence parameter γ(u 2 ; θ) = 1 − exp(−θu 2 ), i.e.,…”

Section: Example 2 (Trivariate Frank Copula)mentioning

confidence: 99%

“…Note that, if the copula of (Y 1:2 , Z) is Archimedean, C Y1,Y2|Z is always Archimedean (Mesfioui and Quessy, 2008).…”

Section: Property 5 (Archimedean Copulas)mentioning

confidence: 99%

The partial copula: Properties and associated dependence measures

Spanhel

Kurz

2016

Statistics & Probability Letters

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“…F(y 1 , y 2 , x) = P(Y 1 ≤ y 1 , Y 2 ≤ y 2 , X ≤ x) = ϕ −1 {ϕ(y 1 ) + ϕ(y 2 ) + ϕ(x)}, where ϕ : [0, 1] → R + is a uni-variate decreasing and convex Archimedean generator. As shown by Mesfioui and Quessy (2008), the joint distribution of (Y 1 , Y 2 ) given X = x has marginal distributions F 1x (y) = F 2x (y) = (ϕ −1 ) {ϕ(y) + ϕ(x)}ϕ (x) and a copula that stays in the Archimedean class, but whose generator is…”

Section: Interval Estimation Of Conditional Kendall's Taumentioning

confidence: 99%

“…For Clayton's copula whose generator is ϕ C θ (t) = (t −θ − 1) /θ , θ > −1, computations in Mesfioui and Quessy (2008) show that the conditional generator is ϕ x = ϕ C θ , where θ = θ/(θ + 1), so that this copula is family-invariant with respect to conditioning. A simple computation shows that τ x (θ ) = θ/(3θ + 2) = τ (θ)/{2τ (θ) + 1}, where τ (θ) = θ/(θ +2) is Kendall's tau associated to ϕ C θ .…”

Section: Interval Estimation Of Conditional Kendall's Taumentioning

confidence: 99%

Multiplier bootstrap methods for conditional distributions

Lemyre

Quessy

2016

Stat Comput

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The multiplier bootstrap is a fast and easy-toimplement alternative to the standard bootstrap; it has been used successfully in many statistical contexts. In this paper, resampling methods based on multipliers are proposed in a general framework where one investigates the stochastic behavior of a random vector Y ∈ R d conditional on a covariate X ∈ R. Specifically, two versions of the multiplier bootstrap adapted to empirical conditional distributions are introduced as alternatives to the conditional bootstrap and their asymptotic validity is formally established. As the method walks hand-in-hand with the functional delta method, theory around the estimation of statistical functionals is developed accordingly; this includes the interval estimation of conditional mean and variance, conditional correlation coefficient, Kendall's dependence measure and copula. Composite inference about univariate and joint conditional distributions is also considered. The sample behavior of the new bootstrap schemes and related estimation methods are investigated via simulations and an illustration on real data is provided.

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“…Another family of copula functions are the so-called "Archimedean" that allow the dependency in high variable dimension to be modeled using only one parameter. Examples of this family are Clayton, Frank, and Gumbel copulas [172]. All of these methods model specific dependency structures, expect GMM, which is able to model many structures of arbitrary dependency.…”

Section: Copula Functionsmentioning

confidence: 99%

New Insights in Prediction and Dynamic Modeling from Non-Gaussian Mixture Processing Methods

Armero¹

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This thesis considers new applications of non-Gaussian mixtures in the framework of statistical signal processing and pattern recognition. The non-Gaussian mixtures were implemented by mixtures of independent component analyzers (ICA). The fundamental hypothesis of ICA is that the observed signals can be expressed as a linear transformation of a set of hidden variables, usually referred to as sources, which are statistically independent. This independence allows factoring the original M-dimensional probability density function (PDF) of the data as a product of one-dimensional probability densities, greatly simplifying the modeling of the data. ICA mixture models (ICAMM) provide further flexibility by alleviating the independency requirement of ICA, thus allowing the model to obtain local projections of the data without compromising its generalization capabilities. Here are explored new possibilities of ICAMM for the purposes of estimation and classification of signals.The thesis makes several contributions to the research in non-Gaussian mixtures: (i) a method for maximum-likelihood estimation of missing data, based on the maximization of the PDF of the data given the ICAMM; (ii) a method for Bayesian estimation of missing data that minimizes the mean squared error and can obtain the confidence interval of the prediction; (iii) a generalization of the sequential dependence model for ICAMM to semi-supervised or supervised learning and multiple chains of dependence, thus allowing the use of multimodal data; and (iv) introduction of ICAMM in diverse novel applications, both for estimation and for classification.The developed methods were validated via an extensive number of simulations that covered multiple scenarios. These tested the sensitivity of the proposed methods with respect to the following parameters: number of values to estimate; kinds of source distributions; correspondence of the data with respect to the assumptions of the model; number of classes in the mixture model; and unsupervised, semi-supervised, and supervised learning. The performance of the proposed methods was evaluated using several figures of merit, and compared with the performance of multiple classical and state-of-the-art techniques for estimation and classification.Aside from the simulations, the methods were also tested on several sets of real data from different types: data from seismic exploration studies; ground penetrating radar surveys; and biomedical data. These data correspond to the following applications: reconstruction of damaged or missing data from ground-penetrating radar surveys of historical walls; reconstruction of damaged or missing data from a seismic exploration survey; reconstruction of artifacted or missing electroencephalographic (EEG) data; diagnosis of sleep disorders; modeling of the brain response during memory tasks; and exploration of EEG data from subjects performing a battery of neuropsychological tests. The obtained results demonstrate the capability of the proposed methods to work on problems wi...

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Dependence structure of conditional Archimedean copulas

Cited by 21 publications

References 15 publications

The partial copula: Properties and associated dependence measures

The partial copula: Properties and associated dependence measures

Multiplier bootstrap methods for conditional distributions

New Insights in Prediction and Dynamic Modeling from Non-Gaussian Mixture Processing Methods

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