Multi-type insurance claim processes with high-dimensional covariates

Multi-type insurance claim processes have attracted considerable research interest in the literature. The existing statistical inference for such processes, however, may encounter “curse of dimensionality” due to high-dimensional covariates. In this article, a technique of sufficient dimension reduction is applied to multiple-type insurance claim data, which uses a copula to model the dependence between different types of claim processes, and incorporates a one-dimensional frailty to fit the dependence of claims “within” the same claim process. A two-step procedure is proposed to estimate model parameters. The first step develops nonparametric estimators of the baseline, the basis of the central subspace and its dimension, and the regression function. Then the second step estimates the copula parameter. Simulations are performed to evaluate and confirm the theoretical results.