  Copula-based modeling has seen rapid advances in recent years. However, in
big data applications, the lengthy computation time for estimating copula
parameters is a major difficulty. Here, we develop a novel method to speed
computation time in estimating copula parameters, using communication-free
parallel computing. Our procedure partitions full data sets into disjoint
independent subsets, performs copula parameter estimation on the subsets, and
combines the results to produce an approximation to the full data copula
parameter. We show in simulation studies that the computation time is greatly
reduced through our method, using three well-known one-parameter bivariate
copulas within the elliptical and Archimedean families: Gaussian, Frank and
Gumbel. In addition, our simulation studies find small values for estimated
bias, estimated mean squared error, and estimated relative L1 and L2 errors for
our method, when compared to the full data parameter estimates.

Methodology