Electronic Journal of Statistics

Multivariate and functional covariates and conditional copulas

Irène Gijbels, Marek Omelka, and Noël Veraverbeke

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In this paper the interest is to estimate the dependence between two variables conditionally upon a covariate, through copula modelling. In recent literature nonparametric estimators for conditional copula functions in case of a univariate covariate have been proposed. The aim of this paper is to nonparametrically estimate a conditional copula when the covariate takes on values in more complex spaces. We consider multivariate covariates and functional covariates. We establish weak convergence, and bias and variance properties of the proposed nonparametric estimators. We also briefly discuss nonparametric estimation of conditional association measures such as a conditional Kendall’s tau. The case of functional covariates is of particular interest and challenge, both from theoretical as well as practical point of view. For this setting we provide an illustration with a real data example in which the covariates are spectral curves. A simulation study investigating the finite-sample performances of the discussed estimators is provided.

Article information

Electron. J. Statist., Volume 6 (2012), 1273-1306.

First available in Project Euclid: 26 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62H20: Measures of association (correlation, canonical correlation, etc.)
Secondary: 62G20: Asymptotic properties

Asymptotic representation empirical copula process functional covariates multivariate covariates small ball probability random design smoothing


Gijbels, Irène; Omelka, Marek; Veraverbeke, Noël. Multivariate and functional covariates and conditional copulas. Electron. J. Statist. 6 (2012), 1273--1306. doi:10.1214/12-EJS712. https://projecteuclid.org/euclid.ejs/1343310298

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