TITLE:
Simulated Minimum Cramér-Von Mises Distance Estimation for Some Actuarial and Financial Models
AUTHORS:
Andrew Luong, Christopher Blier-Wong
KEYWORDS:
Compound Poisson Distribution, Double Exponential Jump Diffusion Distribution, Mixture Distribution, Robustness, Influence Functions
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.5,
October
25,
2017
ABSTRACT: Minimum Cramér-Von Mises distance estimation is
extended to a simulated version. The simulated version consists of replacing
the model distribution function with a sample distribution constructed using a
simulated sample drawn from it. The method does not require an explicit form of
the model density functions and can be applied to fitting many useful
infinitely divisible distributions or mixture distributions without closed form
density functions often encountered in actuarial science and finance. For these
models likelihood estimation is difficult to implement and simulated Minimum
Cramér-Von Mises (SMCVM) distance estimation can be used. Asymptotic properties
of the SCVM estimators are established. The new method appears to be more robust and
efficient than methods of moments (MM) for the models being considered which
have more than two parameters. The method can be used as an alternative to
simulated Hellinger distance (SMHD) estimation with a special feature: it can
handle models with a discontinuity point at the origin with probability mass
assigned to it such as in the case of the compound Poisson distribution where
SMHD method might not be suitable. As the method is based on sample
distributions instead of density estimates it is also easier to implement than
SMHD method but it might not be as efficient as SMHD methods for continuous
models.