 A Family of Goodness†of†Fit Tests for Copulas Based on Characteristic FunctionsTarik Bahraoui, Taoufik Bouezmarni and Jean†François Quessy Scandinavian Journal of Statistics, 2018, vol. 45, issue 2, 301-323 Abstract: A general class of rank statistics based on the characteristic function is introduced for testing goodness†of†fit hypotheses about the copula of a continuous random vector. These statistics are defined as L2 weighted functional distances between a nonparametric estimator and a semi†parametric estimator of the characteristic function associated with a copula. It is shown that these statistics behave asymptotically as degenerate V†statistics of order four and that the limit distributions have representations in terms of weighted sums of independent chi†square variables. The consistency of the tests against general alternatives is established and an asymptotically valid parametric bootstrap is suggested for the computation of the critical values of the tests. The behaviour of the new tests in small and moderate sample sizes is investigated with the help of simulations and compared with a competing test based on the empirical copula. Finally, the methodology is illustrated on a five†dimensional data set. Date: 2018 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:45:y:2018:i:2:p:301-323 Ordering information: This journal article can be ordered from Access Statistics for this article Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association |
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