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Central Limit Theorems for Coupled Particle Filters. (arXiv:1810.04900v1 [math.ST])
来源于:arXiv
In this article we prove a new central limit theorem (CLT) for coupled
particle filters (CPFs). CPFs are used for the sequential estimation of the
difference of expectations w.r.t. filters which are in some sense close.
Examples include the estimation of the filtering distribution associated to
different parameters (finite difference estimation) and filters associated to
partially observed discretized diffusion processes (PODDP) and the
implementation of the multilevel Monte Carlo (MLMC) identity. We develop new
theory for CPFs and based upon several results, we propose a new CPF which
approximates the maximal coupling (MCPF) of a pair of predictor distributions.
In the context of ML estimation associated to PODDP with discretization
$\Delta_l$ we show that the MCPF and the approach in Jasra et al. (2018) have,
under assumptions, an asymptotic variance that is upper-bounded by an
expression that is (almost) $\mathcal{O}(\Delta_l)$, uniformly in time. The
$\mathcal{O}(\Delta_l)$ rate pr 查看全文>>