Mathematics Colloquium: Copula Regression with Discrete Outcomes

2017-02-01

4:10pm Webster Hall 11

Yang Lu

Multivariate discrete outcomes are common in a wide range of areas including insurance, finance, and biology. The interplay between outcomes is often significant, thus quantifying dependencies among interrelated variables is of great importance. Copulas have been increasingly utilized for modeling multivariable outcomes due to their ability of accommodating dependence flexibility. Yet the application of copulas for discrete data is still in its infancy; one of the biggest barriers is the identifiability of copulas, calling into question model interpretations and predictions. We study the issue of identifiability in a regression context and establish the conditions under which copula regression models are identifiable for discrete outcomes. We propose a nonparametric estimator can also serve as a diagnostic tool for selecting a parametric copula and can provide guidance on when the choice of copulas is important. We explore the finite sample performance of our estimator under different scenarios using extensive simulation studies. We then use our model to investigate the dependence of insurance claim frequencies across different business lines using a dataset from the Local Government Property Insurance Fund in the state of Wisconsin. Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)