Derivative Estimation via Simulation in the Presence of Discontinuities

Mikael Signahl

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1404-028X
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.