TITLE:
Simulated Minimum Hellinger Distance Estimation for Some Continuous Financial and Actuarial Models
AUTHORS:
Andrew Luong, Claire Bilodeau
KEYWORDS:
Infinitely Divisible Distribution, Mixture Distribution, Hellinger Distance, Robustness
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.4,
August
31,
2017
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.