Choosing a Copula to Preserve Important Measures of Association

• Activity Number: 603
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Government Statistics
• Author(s): Timothy Keller*+
• Companies: National Agricultural Statistics Service
• Keywords: copula ; synthetic data set

Abstract

Specifying a continuous multivariate distribution requires specifying the marginal distributions and the dependence structure. The latter is completely specified by a copula. A copula not only describes a distribution, but is part of many methods to generate variates following a given distribution. Software to implement these methods is now widely available. The National Agricultural Statistics Service ( NASS ) collects sensitive data for the production of agricultural estimates and to provide agricultural information for data users. NASS must balance the desire to share data with external statistical analysts, and benefit from their viewpoints, with the need for confidentiality. Creating synthetic data sets is a way to achieve this balance, and also provides a tool to conduct realistic simulations studies. We demonstrate that the choice of a copula is critical in preserving relevant measures of association amongst the set of variables of interest.