Inference for intermediate Haezendonck–Goovaerts risk measure

Recently Haezendonck–Goovaerts (H–G) risk measure has received much attention in actuarial science. Nonparametric inference has been studied by Ahn and Shyamalkumar (2014) and Peng et al. (2015) when the risk measure is defined at a fixed level. In risk management, the level is usually set to be quite near one by regulators. Therefore, especially when the sample size is not large enough, it is useful to treat the level as a function of the sample size, which diverges to one as the sample size goes to infinity. In this paper, we extend the results in Peng et al. (2015) from a fixed level to an intermediate level. Although the proposed maximum empirical likelihood estimator for the H–G risk measure has a different limit for a fixed level and an intermediate level, the proposed empirical likelihood method indeed gives a unified interval estimation for both cases. A simulation study is conducted to examine the finite sample performance of the proposed method.