Parallel Computing for Copula Parameter Estimation with Big Data: A Simulation Study

TL;DR

This paper introduces a communication-free parallel computing method to efficiently estimate copula parameters in big data contexts, significantly reducing computation time while maintaining accuracy.

Contribution

The paper presents a novel parallel estimation approach that partitions data, estimates parameters independently, and combines results, improving speed without sacrificing accuracy.

Findings

Computation time is greatly reduced using the proposed method.

Estimated bias and errors are small and comparable to full data estimates.

Method performs well across Gaussian, Frank, and Gumbel copulas.

Abstract

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.