Electronic Journal of Statistics

Multivariate and functional covariates and conditional copulas

Irène Gijbels, Marek Omelka, and Noël Veraverbeke

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 26 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1343310298

Digital Object Identifier
doi:10.1214/12-EJS712

Mathematical Reviews number (MathSciNet)
MR2988448

Zentralblatt MATH identifier
1295.62031

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

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

Citation

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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