An Improved Hazard Rate Twisting Approach for the Statistic of the Sum of Subexponential Variates (Extended Version)

TL;DR

This paper introduces an improved hazard rate twisting method that selectively twists only the most impactful variables in the sum of subexponential RVs, enhancing variance reduction and estimation accuracy for tail probabilities.

Contribution

The paper proposes a selective twisting approach for subexponential RVs, optimizing the twisting parameter via a minmax method for better tail probability estimation.

Findings

Significant variance reduction compared to full twisting methods

Selective twisting improves estimation accuracy for tail probabilities

Method demonstrates asymptotic optimality in simulations

Abstract

In this letter, we present an improved hazard rate twisting technique for the estimation of the probability that a sum of independent but not necessarily identically distributed subexponential Random Variables (RVs) exceeds a given threshold. Instead of twisting all the components in the summation, we propose to twist only the RVs which have the biggest impact on the right-tail of the sum distribution and keep the other RVs unchanged. A minmax approach is performed to determine the optimal twisting parameter which leads to an asymptotic optimality criterion. Moreover, we show through some selected simulation results that our proposed approach results in a variance reduction compared to the technique where all the components are twisted.