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Brownian confidence bands on Monte Carlo output
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Kendall, Wilfrid S., Marin, JeanMichel and Robert, Christian P., 1961 (2005) Brownian confidence bands on Monte Carlo output. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
When considering a Monte Carlo estimation procedure, the path produced by successive partial estimates is often used as a guide for informal convergence diagnostics. However the confidence region associated with that path cannot be derived simplistically from the confidence interval for the estimate itself. An asymptotically correct approach can be based on the Brownian motion approximation of the path, but no exact formula for the corresponding areaminimizing confidence region is yet known. We construct proxy regions based on local time arguments and consider numerical approximations. These are then available for a more incisive assessment of the Monte Carlo procedure and thence of the estimate itself.
Item Type:  Working or Discussion Paper (Working Paper) 

Alternative Title:  Confidence bands for Brownian motion and applications to Monte Carlo simulation 
Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Monte Carlo method, Brownian motion processes 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Date:  2005 
Volume:  Vol.2005 
Number:  No.2 
Number of Pages:  18 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/35579 
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