Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

S.U. Can, John Einmahl, R.J.A. Laeven

Research output: Working paperDiscussion paperOther research output

192 Downloads (Pure)

Abstract

Consider a random sample from a continuous multivariate distribution function
F with copula C. In order to test the null hypothesis that C belongs to a certain
parametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-t tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages33
Volume2017-052
Publication statusPublished - 11 Dec 2017

Publication series

NameCentER Discussion Paper
Volume2017-052

Fingerprint

Distribution-free
Copula
Goodness of fit
Testing
Empirical Process
t-test
Wiener Process
Multivariate Distribution
Continuous Distributions
Null hypothesis
Data analysis
Simulation Study
Generator
Converge
Estimator
Family
Standards

Keywords

  • Khmaladze transform,
  • copula estimation
  • empirical process

Cite this

Can, S. U., Einmahl, J., & Laeven, R. J. A. (2017). Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas. (CentER Discussion Paper; Vol. 2017-052). Tilburg: CentER, Center for Economic Research.
Can, S.U. ; Einmahl, John ; Laeven, R.J.A. / Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas. Tilburg : CentER, Center for Economic Research, 2017. (CentER Discussion Paper).
@techreport{feb9a0642a9f47d6a02b7e5bfeeb9a63,
title = "Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas",
abstract = "Consider a random sample from a continuous multivariate distribution functionF with copula C. In order to test the null hypothesis that C belongs to a certainparametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-t tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.",
keywords = "Khmaladze transform,, copula estimation, empirical process",
author = "S.U. Can and John Einmahl and R.J.A. Laeven",
year = "2017",
month = "12",
day = "11",
language = "English",
volume = "2017-052",
series = "CentER Discussion Paper",
publisher = "CentER, Center for Economic Research",
type = "WorkingPaper",
institution = "CentER, Center for Economic Research",

}

Can, SU, Einmahl, J & Laeven, RJA 2017 'Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas' CentER Discussion Paper, vol. 2017-052, CentER, Center for Economic Research, Tilburg.

Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas. / Can, S.U.; Einmahl, John; Laeven, R.J.A.

Tilburg : CentER, Center for Economic Research, 2017. (CentER Discussion Paper; Vol. 2017-052).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

AU - Can, S.U.

AU - Einmahl, John

AU - Laeven, R.J.A.

PY - 2017/12/11

Y1 - 2017/12/11

N2 - Consider a random sample from a continuous multivariate distribution functionF with copula C. In order to test the null hypothesis that C belongs to a certainparametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-t tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.

AB - Consider a random sample from a continuous multivariate distribution functionF with copula C. In order to test the null hypothesis that C belongs to a certainparametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-t tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.

KW - Khmaladze transform,

KW - copula estimation

KW - empirical process

M3 - Discussion paper

VL - 2017-052

T3 - CentER Discussion Paper

BT - Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

PB - CentER, Center for Economic Research

CY - Tilburg

ER -

Can SU, Einmahl J, Laeven RJA. Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas. Tilburg: CentER, Center for Economic Research. 2017 Dec 11. (CentER Discussion Paper).