Negative association, ordering and convergence of resampling methods

Mathieu Gerber (), Nicolas Chopin and Nick Whiteley ()
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Mathieu Gerber: School of Mathematics, University of Bristol
Nick Whiteley: School of Mathematics, University of Bristol

No 2017-36, Working Papers from Center for Research in Economics and Statistics

Abstract: We study convergence and convergence rates for resampling. Our ?rst main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of measures output from Kitagawa’s (1996) strati?ed resampling method. Carpenter et al’s (1999) systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of Srinivasan (2001), which shares some attractive properties of systematic resampling, but which exhibits negative association and therefore converges irrespective of the order of the input samples. We con?rm a conjecture made by Kitagawa (1996) that ordering input samples by their states in R yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in Rd, the variance of the resampling error is O(N-(1+1/d)) under mild conditions, where N is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that di?er from multinomial resampling.

Keywords: Negative association; resampling; particle ?ltering (search for similar items in EconPapers)
Pages: 54 pages
Date: 2017-07-06
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