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Activity Number: 90
Type: Contributed
Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #308350
Title: A Nonparametric Omnibus Independence Test Based on Copula Density
Author(s): Gery Geenens*+
Companies: UNSW
Keywords: independence test ; copula modelling ; copula density ; kernel density estimation ; boundary bias ; Cramer-von Mises statistics

The concept of independence is central in statistics, and being able to test for the independence of two random variables X and Y is of course very important. We propose an independence test which is able to detect any departure from the null hypothesis of independence (omnibus) between two continuous random variables X and Y and which does not rely on any particular parametric assumptions on the distributions of X and Y (nonparametric). It is based on copula density estimation. Specifically, the test statistic is a Cramer-von Mises-type discrepancy measure between a (boundary-bias-corrected) kernel estimate of the copula density of (X,Y) and the independence copula density. Basing an independence test on the copula density has numerous advantages that will be discussed during the talk, and the resulting test turns out to be very powerful at detecting subtle departures from independence in any direction. This is explained through theoretical considerations and illustrated by substantial simulation studies.

Authors who are presenting talks have a * after their name.

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