Clustered Coefficient Regression Models for Poisson Process with an Application to Seasonal Warranty Claim Data

Motivated by a product warranty claims dataset, we propose clustered coefficient regression models in a nonhomogeneous Poisson process for recurrent event data. The proposed method, referred as CLUPP, can estimate the group structure and parameters simultaneously. In our proposed method, a penalized regression approach is used to identify the group structure. Numerical studies show that the proposed approach can identify the group structure well, and outperforms traditional methods such as hierarchical clustering and <i>K</i>-means. We also establish theoretical properties, which show that the proposed estimators can converge to true parameters in high probability. In the end, we apply our proposed methods to the product warranty claims dataset, which achieve better prediction than the state-of-the-art methods.