Note: On the Interchange of Derivative and Expectation for Likelihood Ratio Derivative Estimators

Pierre L'Ecuyer
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Pierre L'Ecuyer: Départment d'I.R.O., Université de Montréal, C. P. 6128, Montréal, Quebec, Canada H3C 3J7

Management Science, 1995, vol. 41, issue 4, 738-747

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

Keywords: derivative estimation; likelihood ratio (search for similar items in EconPapers)
Date: 1995
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