Derivative Estimation via Simulation in the Presence of Discontinuities
Mikael Signahl
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2001
ISSN 1404028X

Abstract:

In this paper we address the problem of estimating the mean derivative when
the entity containing the parameter has jumps. The methods considered are
finite differences, infinitesimal perturbation analysis and the likelihood
ratio score function. We calculate the difference between the differentiated
mean and the mean derivative when the two operations do not commute. In case
of finite differences, we compute the stepsize in the simulation that
asymptotically minimize the mean square error. We also show that the two
latter methods, infinitesimal perturbation analysis and likelihood ratio
score function, are mathematically equivalent.
