×
Tanizaki, Hisashi

Nonlinear and non-Gaussian state estimation: A quasi-optimal estimator. (English) Zbl 1016.93068

Commun. Stat., Theory Methods 29, No. 12, 2805-2834 (2000).
The author considers a nonlinear and non-Gaussian state space model which is described by the following two equations: \[ y_t= h_t(\alpha_t, \varepsilon_t),\quad \alpha_t= f_t(\alpha_{t-1}, \eta_t), \] where \(y_t\) represents the observed data at time \(t\) while \(\alpha_t\) denotes the state vector, \(\varepsilon_t\) and \(\eta_t\) are mutually independently distributed. The problem is to estimate \(\alpha_t\) given \(Y_s= \{y_1,y_2,\dots, y_s\}\). The author proposes a quasi-optimal filtering and smoothing procedure which shows a good performance in the sense of the root mean square error criterion and improves computational disadvantages of some known procedures.
Reviewer: Grigori Milstein (Berlin)

Cited in 2 Documents

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
65C05 Monte Carlo methods

Keywords:

Monte Carlo procedure; Metropolis-Hastings algorithm; nonlinear filtering; quasi-optimal smoothing; non-Gaussian state space model; quasi-optimal filtering; root mean square error criterion
Cite Review PDF
Full Text: DOI

References:

[1] Anderson B.D.O., Optimal Filtering (1979)
[2] Arnold S.F., in Handbook of Statistics 9 pp 599– (1993)
[3] Berzuini C., Journal of the American Statistical Association 921997 pp 1403–
[4] Bollerslev T., in Handbook of Econometrics 4 pp 2959– (1994)
[5] Boswell M.T., in Handbook of Statistics 9 pp 661– (1993)
[6] DOI: 10.2307/2290282 · doi:10.2307/2290282
[7] DOI: 10.1093/biomet/81.3.541 · Zbl 0809.62087 · doi:10.1093/biomet/81.3.541
[8] DOI: 10.1093/biomet/83.3.589 · Zbl 0866.62018 · doi:10.1093/biomet/83.3.589
[9] DOI: 10.2307/2684568 · doi:10.2307/2684568
[10] DOI: 10.1017/S0266466600006794 · doi:10.1017/S0266466600006794
[11] DOI: 10.1093/biomet/84.3.669 · Zbl 0888.62086 · doi:10.1093/biomet/84.3.669
[12] DOI: 10.2307/1912773 · Zbl 0491.62099 · doi:10.2307/1912773
[13] Gelb A., Applied Optimal Estimation (1974)
[14] DOI: 10.2307/2289776 · Zbl 0702.62020 · doi:10.2307/2289776
[15] DOI: 10.1109/TPAMI.1984.4767596 · Zbl 0573.62030 · doi:10.1109/TPAMI.1984.4767596
[16] Geweke J., in Handbook of Computational Economics 1 pp 731– (1996)
[17] Geweke J., in Advances in Economics and Econometrics: Theory and Applications 3 pp 128– (1997) · doi:10.1017/CBO9781139051996.005
[18] DOI: 10.1080/03610919908813583 · Zbl 0968.62541 · doi:10.1080/03610919908813583
[19] Geweke J., Unpublished Manuscript (1999)
[20] Ghysels E., in Handbook of Statistics 14 pp 119– (1996)
[21] Gordon N.J., IEE Proceedings-F 140 pp 107– (1993)
[22] Harvey A.C., Forecasting, Structural Time Series Models and the Kalman Filter (1989)
[23] DOI: 10.2307/1390812 · doi:10.2307/1390812
[24] DOI: 10.2307/2289375 · Zbl 0644.62088 · doi:10.2307/2289375
[25] DOI: 10.2307/1390750 · doi:10.2307/1390750
[26] DOI: 10.1007/978-1-4612-0761-0 · Zbl 0853.62069 · doi:10.1007/978-1-4612-0761-0
[27] DOI: 10.2307/2669862 · doi:10.2307/2669862
[28] DOI: 10.2307/2291068 · Zbl 0826.62062 · doi:10.2307/2291068
[29] DOI: 10.2307/2669846 · Zbl 1064.65501 · doi:10.2307/2669846
[30] DOI: 10.2307/2669847 · Zbl 1064.65500 · doi:10.2307/2669847
[31] DOI: 10.2307/3315637 · Zbl 0957.62068 · doi:10.2307/3315637
[32] Mariano R.S., forthcoming in Simulation-Based Inference in Econometrics: Methods and Applications (1998)
[33] O’Hagan A., Kendall’s Advanced Theory of Statistics 2 (1994)
[34] Smith A.F.M., Journal of the Royal Statistical Society, Ser.B 55 pp 3– (1993)
[35] Tanizaki H., Nonlinear Filters: Estimation and Applications (1993) · doi:10.1007/978-3-662-22237-9
[36] Tanizaki H., Nonlinear Filters: Estimation and Applications (1996) · doi:10.1007/978-3-662-03223-7
[37] DOI: 10.1109/9.746257 · Zbl 0958.93093 · doi:10.1109/9.746257
[38] DOI: 10.1080/03610929608831763 · Zbl 0875.62436 · doi:10.1080/03610929608831763
[39] DOI: 10.1016/S0304-4076(97)80226-6 · Zbl 0905.62094 · doi:10.1016/S0304-4076(97)80226-6
[40] DOI: 10.2307/2289457 · Zbl 0619.62029 · doi:10.2307/2289457
[41] DOI: 10.1214/aos/1176325750 · Zbl 0829.62080 · doi:10.1214/aos/1176325750
[42] DOI: 10.1016/0005-1098(69)90110-1 · Zbl 0214.47303 · doi:10.1016/0005-1098(69)90110-1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.