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Brownian Confidence Bands on Monte Carlo Output

W.S. Kendall 1 Jean-Michel Marin 1 C.P. Robert
1 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
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 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.
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https://hal.inria.fr/inria-00070571
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Submitted on : Friday, May 19, 2006 - 8:54:43 PM
Last modification on : Wednesday, September 16, 2020 - 5:07:08 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:29:29 PM

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W.S. Kendall, Jean-Michel Marin, C.P. Robert. Brownian Confidence Bands on Monte Carlo Output. Statistics and Computing, Springer Verlag (Germany), 2007, 17 (1), pp.1-10. ⟨inria-00070571⟩

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