The Bernstein Copula and Its Applications to Modeling and Approximations of Multivariate Distributions

Sancetta, Alessio; Satchell, Stephen

doi:10.1017/s026646660420305x

Cited by 228 publications

(203 citation statements)

References 17 publications

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“…In that case, the joint default probability rewrites as an integral over the expectation of a polynomial in a polynomial di usion which is an analytical expression, see [20]. Some examples of polynomial copulas, such as the Farlie-Gumbel-Morgenstern copula, can be found in [44] and the Bernstein copulas, which can approximate any copula, are studied in [47].…”

Section: Lemma 32 the Probability Distribution Of The Portfolio Losmentioning

confidence: 99%

Dependent defaults and losses with factor copula models

Ackerer¹,

Vatter

2017

Dependence Modeling

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Abstract:We present a class of exible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with paircopula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and e ciently computed when individual losses are discretely supported on a nite grid. Numerical examples study the key features a ecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the exibility of our approach by tting credit index tranche prices.

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Section: Lemma 32 the Probability Distribution Of The Portfolio Losmentioning

confidence: 99%

Dependent defaults and losses with factor copula models

Ackerer¹,

Vatter

2017

Dependence Modeling

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“…See Nelsen (1999) and Joe (1997) for comprehensive references. Flexible families may be constructed, for example by relying on the Bernstein family of polynomials (Sancetta and Satchell, 2004). In all these examples, one may let the vector ρ depend on x.…”

Section: Estimationmentioning

confidence: 99%

Quantile selection models: with an application to understanding changes in wage inequality

Arellano

Bonhomme

2015

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We propose a method to correct for sample selection in quantile regression models. Selection is modelled via the cumulative distribution function, or copula, of the percentile error in the outcome equation and the error in the participation decision. Copula parameters are estimated by minimizing a method-of-moments criterion. Given these parameter estimates, the percentile levels of the outcome are re-adjusted to correct for selection, and quantile parameters are estimated by minimizing a rotated "check" function. We apply the method to correct wage percentiles for selection into employment, using data for the UK for the period 1978-2000. We also extend the method to account for the presence of equilibrium effects when performing counterfactual exercises.JEL code: C13, J31.

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“…For i.i.d. data, Sancetta and Satchell (2004) show that, under some regularity conditions, any copula can be represented by a Bernstein copula. Bouezmarni, Rombouts, and Taamouti (2010) provide the asymptotic properties of the Bernstein copula density estimator for dependent data.…”

Section: Introductionmentioning

confidence: 97%

Nonparametric estimation and inference for conditional density based Granger causality measures

Taamouti

Bouezmarni

Ghouch

2014

Journal of Econometrics

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Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Econometrics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Journal of Econometrics, 180, 2, June 2014, 10.1016/j.jeconom.2014.03.001. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACTWe propose a nonparametric estimation and inference for conditional density based Granger causality measures that quantify linear and nonlinear Granger causalities. We first show how to write the causality measures in terms of copula densities. Thereafter, we suggest consistent estimators for these measures based on a consistent nonparametric estimator of copula densities. Furthermore, we establish the asymptotic normality of these nonparametric estimators and discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap bias-corrected estimator behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, two empirical applications are considered to illustrate the practical relevance of nonparametric causality measures.JEL Classification: C12; C14; C15; C19; G1; G12; E3; E4.

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The Bernstein Copula and Its Applications to Modeling and Approximations of Multivariate Distributions

Cited by 228 publications

References 17 publications

Dependent defaults and losses with factor copula models

Dependent defaults and losses with factor copula models

Quantile selection models: with an application to understanding changes in wage inequality

Nonparametric estimation and inference for conditional density based Granger causality measures

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