Risk analysis with categorical explanatory variables

To better forecast the Value-at-Risk of the aggregate insurance losses, Heras et al. (2018) propose a two-step inference of using logistic regression and quantile regression without providing detailed model assumptions, deriving the related asymptotic properties, and quantifying the inference uncertainty. This paper argues that the application of quantile regression at the second step is not necessary when explanatory variables are categorical. After describing the explicit model assumptions, we propose another two-step inference of using logistic regression and the sample quantile. Also, we provide an efficient empirical likelihood method to quantify the uncertainty. A simulation study confirms the good finite sample performance of the proposed method.