Estimation of Spectral Risk Measures

TL;DR

This paper introduces a new numerical integration-based method for estimating spectral risk measures from samples, providing exponential concentration bounds for bounded support and specific distributions, validated through simulations and traffic routing applications.

Contribution

A novel estimation technique for spectral risk measures with proven concentration bounds for various distribution types.

Findings

Exponential concentration for bounded support distributions

Concentration bounds for Gaussian and exponential distributions

Validated effectiveness through synthetic and real-world traffic data

Abstract

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