On the Convergence Rates of IPA and FDC Derivative Estimators

Pierre L'Ecuyer and Gaétan Perron
Additional contact information
Pierre L'Ecuyer: University of Montreal, Montreal, Canada
Gaétan Perron: GESPRO Informatique, Ste. Foy, Quebec, Canada

Operations Research, 1994, vol. 42, issue 4, 643-656

Abstract: We show that under the (sufficient) conditions usually given for infinitesimal perturbation analysis (IPA) to apply for derivative estimation, a finite-difference scheme with common random numbers (FDC) has the same order of convergence, namely O ( n −1/2 ), provided that the size of the finite-difference interval converges to zero fast enough. This holds for both one- and two-sided FDC. This also holds for different variants of IPA, such as some versions of smoothed perturbation analysis (SPA), which is based on conditional expectation. Finally, this also holds for the estimation of steady-state performance measures by truncated-horizon estimators, under some ergodicity assumptions. Our developments do not involve monotonicity, but are based on continuity and smoothness. We give examples and numerical illustrations which show that the actual difference in mean square error (MSE) between IPA and FDC is typically negligible. We also obtain the order of convergence of that difference, which is faster than the convergence of the MSE to zero.

Keywords: simulation: derivative estimation; sensitivity analysis (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.42.4.643 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:42:y:1994:i:4:p:643-656

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().