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Recursive Monte Carlo filters: Algorithms and theoretical analysis
Open accessAbstract
Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept–reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept–reject version, and we compare different resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that, under stronger conditions, the required sample size is independent of the length of the observed series.
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Cites
Forecasting, Structural Time Series Models and the Kalman Filter
Harvey, A. C. (1990) · doi:10.1017/cbo9781107049994 · Cited by 4,195
Cited by
Sequential Monte Carlo Samplers
Del Moral, P., Doucet, A., & Jasra, A. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2006.00553.x · Cited by 1,239
Parameter estimation for differential equations: a generalized smoothing approach
Ramsay, J. O., Hooker, G., Campbell, D., & Cao, J. (2007) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2007.00610.x · Cited by 613
A Survey of Sequential Monte Carlo Methods for Economics and Finance
Creal, D. (2012) · Econometric Reviews · doi:10.1080/07474938.2011.607333 · Cited by 301
On sequential Monte Carlo, partial rejection control and approximate Bayesian computation
Peters, G. W., Fan, Y., & Sisson, S. A. (2012) · Statistics and Computing · doi:10.1007/s11222-012-9315-y · Cited by 69
Metadata
- Authors
- Künsch, H. R.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2005-10-01
- Volume
- 33
- Issue
- 5
- Pages
- 1983-2021
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2140322433
- Cited by
- 182
- References
- 1
- FWCI
- 8.43
- Type
- journal article
- Language
- en
- Open access
- bronze
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