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Activity Number: 181
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #320064 View Presentation
Title: The Empirical Beta and Bernstein Copula
Author(s): Hideatsu Tsukahara* and Johan Segers and Masaaki Sibuya and Nathan Uyttendaele
Companies: Seijo University and Universite Catholique de Louvain and Keio University and Universite Catholique de Louvain
Keywords: copula ; empirical copula ; Bernstein polynomial ; Bernstein copula
Abstract:

Applying Baker's construction of copulas based on the order statistics with the ranks being coefficients leads us to define the empirical beta copula. It turns out that the empirical beta copula is a particular case of the empirical Bernstein copula. The advantage is that we do not need to choose the value of the smoothing parameters. Also it is extremely simple to simulate a sample from the empirical beta copula. We show that the empirical Bernstein copula is a genuine copula by providing (necessary and) sufficient conditions for a Bernstein transformation to be a copula. Furthermore, we establish the assumptions under which the standard asymptotic results hold for the empirical Bernstein copula. They are significantly weaker than those given in the literature. Our Monte Carlo simulation study shows that there is an advantage of smoothing to improve finite-samples performance.It is found that in all cases, the empirical beta copula outperforms the empirical copula in terms of the bias and the integrated mean squared error. Compared with the empirical Bernstein copula with the optimal smoothing rate in terms of MSE, its performance is still significantly better in several cases.


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

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