Simulated Minimum Hellinger Distance Estimation for Some Continuous Financial and Actuarial Models

Abstract

Minimum Hellinger distance (MHD) estimation is extended to a simulated version with the model density function replaced by a density estimate based on a random sample drawn from the model distribution. The method does not require a closed-form expression for the density function and appears to be suitable for models lacking a closed-form expression for the density, models for which likelihood methods might be difficult to implement. Even though only consistency is shown in this paper and the asymptotic distribution remains an open question, our simulation study suggests that the methods have the potential to generate simulated minimum Hellinger distance (SMHD) estimators with high efficiencies. The method can be used as an alternative to methods based on moments, methods based on empirical characteristic functions, or the use of an expectation-maximization (EM) algorithm.