Brownian confidence bands on Monte Carlo output
Kendall, Wilfrid S., Marin, Jean-Michel 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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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 area-minimizing 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|
|Number of Pages:||18|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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