We develop statistical inferential tools for estimating and comparing conditional tail
expectation (CTE) functions, which are of considerable interest in actuarial science. In
particular, we construct estimators for the CTE functions, develop the necessary asymptotic
theory for the estimators, and then use the theory for constructing confidence intervals and
bands for the functions. Both parametric and non-parametric approaches are explored.
Simulation studies illustrate the performance of estimators in various situations. Results are …