Estimation and asymptotics for buffered probability of exceedance

This paper studies statistical properties of empirical (sample) estimates of the buffered probability of exceedance (bPOE). The estimation procedure is based on one dimensional minimization representation of the bPOE. Convergence rates and asymptotic properties of the suggested estimation procedures are investigated. Theoretical predictions are validated with numerical experiments, including a special case of exponential distribution, and a study proposing bPOE modification of minimum volume ellipsoid problem.