Sharp failure rates for the bootstrap particle filter in high dimensions

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dc.creatorBickel, Peter
dc.creatorLi, Bo
dc.creatorBengtsson, Thomas
dc.date2008-05-21
dc.date.accessioned2026-07-07T12:19:10Z
dc.date.available2026-07-07T12:19:10Z
dc.descriptionWe prove that the maximum of the sample importance weights in a high-dimensional Gaussian particle filter converges to unity unless the ensemble size grows exponentially in the system dimension. Our work is motivated by and parallels the derivations of Bengtsson, Bickel and Li (2007); however, we weaken their assumptions on the eigenvalues of the covariance matrix of the prior distribution and establish rigorously their strong conjecture on when weight collapse occurs. Specifically, we remove the assumption that the nonzero eigenvalues are bounded away from zero, which, although the dimension of the involved vectors grow to infinity, essentially permits the effective system dimension to be bounded. Moreover, with some restrictions on the rate of growth of the maximum eigenvalue, we relax their assumption that the eigenvalues are bounded from above, allowing the system to be dominated by a single mode.
dc.descriptionPublished in at http://dx.doi.org/10.1214/074921708000000228 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0805.3287
dc.identifierhttp://arxiv.org/abs/0805.3287
dc.identifierIMS Collections 2008, Vol. 3, 318-329
dc.identifierdoi:10.1214/074921708000000228
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212658
dc.subjectStatistics Theory
dc.subjectMethodology
dc.subject93E11, 62L12, 86A22, 60G50, 86A32, 86A10 (Primary)
dc.titleSharp failure rates for the bootstrap particle filter in high dimensions
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