Copula modeling for data with ties

摘要

Tied observations in copula modeling may cause serious problems to rank-based inference methods that are intended for data with no ties. Simple methods such as breaking the ties at random or using midrank could lead to bias in estimation and invalidity in naive bootstrap inferences. We propose to treat the ranks of tied observations as being interval censored and estimate the copula parameters by maximizing a pseudo-likelihood based on interval censored pseudo-observations. A parametric bootstrap procedure that preserves the tied ranks in the observed data is adapted to do interval estimation and goodness-of-fit test. The proposed approach is shown to be very competitive in comparison to the simple treatments in a large scale simulation study. The utility of the method is illustrated in real data examples.