NOTE - ON THE INTERCHANGE OF DERIVATIVE AND EXPECTATION FOR LIKELIHOOD RATIO DERIVATIVE ESTIMATORS

Sufficient conditions for the validity of interchange between derivati ve and expectation, in the context of likelihood ratio gradient estima tion, were given in L'Ecuyer (1990). The aim of this paper is to shed additional light on these conditions and introduce specific variants o f them, which are often easier to check. Sufficient conditions for the derivative estimator to have finite moments up to a given order are a lso given and illustrated by examples. In particular, we give an examp le of an unbiased derivative estimator which satisfies the interchange conditions but which has infinite variance.