Estimation of Spectral Risk Measures

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose novel method that is based on numerical integration. show our SRM estimate concentrates exponentially, when underlying distribution has bounded support. Further, we also case satisfies an exponential moment bound, which includes sub-Gaussian subexponential distributions. For these distributions, derive concentration bound for estimation scheme. validate theoretical findings synthetic setup, in vehicular traffic routing application.