Paper Info
Title
The empirical beta copula.
Abstract
Given a sample from a continuous multivariate distribution F , the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of F . This idea can be regarded as a variant on Baker's J. Multivariate Anal. 99 (2008) 2312-2327 copula construction and leads to the definition of the empirical beta copula. The latter turns out to be a particular case of the empirical Bernstein copula, the degrees of all Bernstein polynomials being equal to the sample size.Necessary and sufficient conditions are given for a Bernstein polynomial to be a copula. These imply that the empirical beta copula is a genuine copula. Furthermore, the empirical process based on the empirical Bernstein copula is shown to be asymptotically the same as the ordinary empirical copula process under assumptions which are significantly weaker than those given in Janssen, Swanepoel and Veraverbeke J. Statist. Plann. Inference 142 (2012) 1189-1197.A Monte Carlo simulation study shows that the empirical beta copula outperforms the empirical copula and the empirical checkerboard copula in terms of both bias and variance. Compared with the empirical Bernstein copula with the smoothing rate suggested by Janssen et al., its finite-sample performance is still significantly better in several cases, especially in terms of bias.
Year
DOI
Venue
2017
10.1016/j.jmva.2016.11.010
J. Multivariate Analysis
Keywords
Field
DocType
62G20,62G30,62H12
Econometrics,Monte Carlo method,Copula (linguistics),Multivariate statistics,Inference,Multivariate normal distribution,Bernstein polynomial,Smoothing,Beta (finance),Statistics,Mathematics
Journal
Volume
Issue
ISSN
155
C
0047-259X
Citations 
PageRank 
References 
2
0.49
1
Authors
3
Name
Order
Citations
PageRank
Johan Segers14110.37
Masaaki Sibuya232.92
Hideatsu Tsukahara320.49