Smoothing complements and randomized score functions
type: Item
instance of: scholarly article
title: Smoothing complements and randomized score functions
zbMATH Open document ID: 0771.62024
DOI: 10.1007/BF02060935
author: Paul Glasserman
published in: Annals of Operations Research
publication date: 1993-05-16T00:00:00Z
review text: Let \(({\mathcal X},{\mathcal A})\) be a measurable space and \(\{P_ \theta, \theta\in\Theta\}\) be a family of probability measures defined on \(({\mathcal X},{\mathcal A})\). Let \(T(\cdot)\) be a real-valued measurable function on \({\mathcal X}\) and define \(g(\theta)=E_ \theta[\Gamma(x)]\). Assume that \(g(\theta)\) is differentiable with respect to \(\theta\) and denote the derivative by \(g'(\theta)\). This paper studies connections between the infinitesimal perturbation analysis (IPA) and the likelihood ratio or score function method for estimation of \(g(\theta)\). The author shows that likelihood ratio derivative estimators are IPA estimators obtained through a special construction based on the notion of multiplicative smoothing. (Reviewer's remarks: The concepts used in this area seem to differ from the standard definitions in the areas of statistics and probability. This is illustrated for instance by the fact that estimators cannot be considered as a function of the unknown parameter \(\theta\) as in classical statistics, see page 42, line 3.) Multiplicative smoothing in some sense enlarges the probability space whereas conditioning ``shrinks'' it.
reviewed by: B. L. S. Prakasa Rao
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 62P99
zbMATH DE Number: 165329
zbMATH Keywords: smoothing complement
zbMATH Keywords: indirect derivative estimator
zbMATH Keywords: randomized score function
zbMATH Keywords: conditional expectation
zbMATH Keywords: infinitesimal perturbation analysis
zbMATH Keywords: score function method
zbMATH Keywords: likelihood ratio derivative estimators
zbMATH Keywords: IPA estimators
zbMATH Keywords: multiplicative smoothing
zbMATH Keywords: conditioning
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 165329