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A1678
Title: Copula by triangulation, with application to tail dependence estimation Authors:  Artem Prokhorov - University of Sydney (Australia) [presenting]
Yajing Zhu - Concordia University (Canada)
Edward Anderson - University of Sydney (Australia)
Abstract: Copulas are distributions with uniform marginals. The uniformity condition is a key copula property which is hard to impose in estimation. Many nonparametric estimators suffer from poor finite sample properties due to violations of this condition. We develop a new $B-$spline estimator of a general bivariate copula based on triangulation, which ensures that marginals are uniform by construction. We look at the properties of the new estimator, both asymptotically and in finite samples, and compare it with available alternatives such as the Kantorovich-Bernstein sieve estimator, Data-Mirror and Exponential Series estimators. The new estimator dominates the alternatives in terms of MSE and computational efficiency. We also show that violations of the uniformity condition lead to severely distorted estimates of the tail dependence coefficient. These biases can be corrected by using the new copula estimator.