1 research outputs found
Negative association, ordering and convergence of resampling methods
We study convergence and convergence rates for resampling schemes. Our first
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) stratified 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 confirm a conjecture made by Kitagawa (1996)
that ordering input samples by their states in yields a faster
rate of convergence; we establish that when particles are ordered using the
Hilbert curve in , the variance of the resampling error is
under mild conditions, where
is the number of particles. We use these results to establish asymptotic
properties of particle algorithms based on resampling schemes that differ from
multinomial resampling.Comment: 54 pages, including 30 pages of supplementary materials (a typo in
Algorithm 1 has been corrected