## Bernoulli

• Bernoulli
• Volume 10, Number 5 (2004), 847-860.

### Weak convergence of empirical copula processes

#### Abstract

Weak convergence of the empirical copula process has been established by Deheuvels in the case of independent marginal distributions. Van der Vaart and Wellner utilize the functional delta method to show convergence in $\ell^\infty([a,b]^2)$> for some 0<a<b<1, under restrictions on the distribution functions. We extend their results by proving the weak convergence of this process in $\ell^\infty([0,1]^2)$> under minimal conditions on the copula function, which coincides with the result obtained by Gaenssler and Stute. It is argued that the condition on the copula function is necessary. The proof uses the functional delta method and, as a consequence, the convergence of the bootstrap counterpart of the empirical copula process follows immediately. In addition, weak convergence of the smoothed empirical copula process is established.

#### Article information

Source
Bernoulli Volume 10, Number 5 (2004), 847-860.

Dates
First available in Project Euclid: 4 November 2004

Permanent link to this document
http://projecteuclid.org/euclid.bj/1099579158

Digital Object Identifier
doi:10.3150/bj/1099579158

Mathematical Reviews number (MathSciNet)
MR2093613

Zentralblatt MATH identifier
02149083

#### Citation

Fermanian, Jean-David; Radulovic, Dragan; Wegkamp, Marten. Weak convergence of empirical copula processes. Bernoulli 10 (2004), no. 5, 847--860. doi:10.3150/bj/1099579158. http://projecteuclid.org/euclid.bj/1099579158.

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