Data mining procedures in generalized Cox regressions

Survival (default) data are frequently encountered in financial (especially credit risk), medical, educational, and other fields, where the “default” can be interpreted as the failure to fulfill debt payments of a specific company or the death of a patient in a medical study or the inability to pass some educational tests. This paper introduces the basic ideas of Cox's original proportional model for the hazard rates and extends the model within a general framework of statistical data mining procedures. By employing regularization, basis expansion, boosting, bagging, Markov chain Monte Carlo (MCMC) and many other tools, we effectively calibrate a large and flexible class of proportional hazard models. The proposed methods have important applications in the setting of credit risk. For example, the model for the default correlation through regularization can be used to price credit basket products, and the frailty factor models can explain the contagion effects in the defaults of multiple firms in the credit market.