Copula Modeling for Data with Ties

TL;DR

This paper introduces a novel copula modeling method for data with ties by treating tied ranks as interval censored, improving estimation accuracy and providing a bootstrap-based goodness-of-fit assessment.

Contribution

It proposes a new estimation approach for copulas with tied data using interval censoring and develops a bootstrap procedure for uncertainty quantification and model testing.

Findings

Method outperforms simple tie-breaking techniques in simulations.

Bootstrap procedure effectively assesses estimation uncertainty.

Application demonstrates practical utility in insurance data.

Abstract

Copula modeling has gained much attention in many fields recently with the advantage of separating dependence structure from marginal distributions. In real data, however, serious ties are often present in one or multiple margins, which cause problems to many rank-based statistical methods developed under the assumption of continuous data with no ties. Simple methods such as breaking the ties at random or using average rank introduce independence into the data and, hence, lead to biased estimation. We propose an estimation method that treats the ranks of tied data as being interval censored and maximizes a pseudo-likelihood based on interval censored pseudo-observations. A parametric bootstrap procedure that preserves the observed tied ranks in the data is adapted to assess the estimation uncertainty and perform goodness-of-fit tests. The proposed approach is shown to be very competitive in comparison to the simple treatments in a large scale simulation study. Application to a bivariate insurance data illustrates the methodology.