Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Chapter EightModel Selection and Goodness-of-Fit Testing for Frequency and Severity Models

In this chapter, we present details on statistical approaches to performing model selection. We separate the sections first into diagnostic tools that may be adopted to make quantitative assessments for model selection purposes. This includes analysis of the presence of heavy-tailed features of the data. Then the focus of the next few sections is on individual risk process model selections under a Loss Distribution Approach (LDA) structure, for the severity model and the frequency models. This can be achieved under a number of different frameworks such as information criteria, frequentist hypothesis testing, and Bayesian model selection approaches. A particular focus in these sections involves the suitable modifications to classical hypothesis tests that should be considered when performing model selection on heavy-tailed models, for instance, for the severity distribution. This is important to consider as it can have a substantial impact on the choice of the model and therefore on the capital. The last sections of this chapter involve the model selection of dependence features between multiple risks, such as model selection for the copula distribution, which may be used to link multiple risk processes as discussed in detail in Chapters 10–12.

8.1 Qualitative Model Diagnostic Tools

In general, it is often practical to utilize a range of model diagnostic tools to make qualitative judgments ...