[Ml-stat-talks] Wilks Statistics Seminar: Marten Wegkamp (Cornell)

Philippe Rigollet rigollet at Princeton.EDU
Fri Apr 19 12:28:51 EDT 2013

This is NOW in Sherrerd Hall, rm 101.

An Asymptotic Total Variation Test for Copulas

We propose a new goodness-of-t test for copulas, based on empirical copula processes
and their nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type
test for copulas that takes the supremum of the empirical copula process indexed by half
spaces is extended by test statistics based on the supremum of the empirical copula process
indexed by partitions of Ln rectangles with Ln slowly tending to innity. Although the
underlying empirical process does not converge, we prove that the p-values of the new test
statistic can be consistently estimated by the bootstrap. Simulations conrms that the new
procedure often outperforms more common goodness of t tests for copulas.
If time permits, I will discuss some new results on optimal estimation of the copula
correlation matrix of elliptical copulas.
Philippe Rigollet

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