Estimation of unknown parameters in nonlinear and non-Gaussian state-space models

Journal of Statistical Planning and Inference

Volumn 96, Issue 2, 2001, Pages 301-323

  Tanizaki, Hisashi ^a  

^a KOBE UNIVERSITY   (Japan)

Author keywords

62M10; 62M20; Metropolis Hastings algorithm; Mode estimation; Monte Carlo optimization; Nonparametric density estimation; Simulated annealing; State space model

Indexed keywords

EID: 0035402237     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(00)00218-4     Document Type: Article

References (45)

1. Arnold S.F. Gibbs sampling. Rao C.R. Handbook of Statistics, Vol. 9. 1993;599-625 North-Holland, Amsterdam.
2. Bohachevsky I.O., Johnson M.E., Stein M.L. Generalized simulated annealing for function optimization. Technometrics. 28(3):1986;209-217.
3. Bollerslev T., Engle R.F., Nelson D.B. ARCH models. Engle R.F., McFadden D.L. Handbook of Econometrics, Vol. 4. 1994;2959-3038 North-Holland, Amsterdam.
4. Boswell M.T., Gore S.D., Patil G.P., Taillie C. The art of computer generation of random variables. Rao C.R. Handbook of Statistics, Vol. 9. 1993;661-721 North-Holland, Amsterdam.
5. Brooks S.P., Morgan B.J.T. Optimization using simulated annealing. The Statistician. 44(2):1995;241-257.
6. Carlin B.P., Polson N.G., Stoffer D.S. A Monte Carlo approach to nonnormal and nonlinear state space modeling. J. Amer. Statist. Assoc. 87(418):1992;493-500.
7. Carter C.K., Kohn R. On Gibbs sampling for state space models. Biometrika. 81(3):1994;541-553.
8. Carter C.K., Kohn R. Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika. 83(3):1996;589-601.
9. Chan K.S., Ledolter J. Monte Carlo EM estimation for time series models involving counts. J. Amer. Statist. Assoc. 90(429):1995;242-252.
10. Chib S., Greenberg E. Understanding the Metropolis-Hastings Algorithm. Amer. Statist. 49(4):1995;327-335.
11. Chib S., Greenberg E. Markov chain Monte Carlo simulation methods in econometrics. Econometric Theory. 12(4):1996;409-431.
12. Engle R.F. Autoregressive conditional heteroscedasticity with estimates of variance of UK inflation. Econometrica. 50:1982;987-1008.
13. Gelfand A.E., Smith A.F.M. Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85(410):1990;398-409.
14. Geman, S., Geman, D., 1984. Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. Pami-6 (6), 721-741.
15. Geweke, J., 1991. Efficient simulation from the multivariate normal and student- t distributions subject to linear constraints. In: Keramidas, E.M. (Ed.), Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 571-578.
16. Geweke J. Monte Carlo simulation and numerical integration. Amman H.M., Kendrick D.A., Rust J. Handbook of Computational Economics, Vol. 1. 1996;731-800 North-Holland, Amsterdam.
17. Geweke J. Posterior simulators in econometrics. Kreps D., Wallis K.F. Advances in Economics and Econometrics: Theory and Applications, Vol. 3. 1997;128-165 Cambridge University Press, Cambridge.
18. Geweke J., Tanizaki H. On Markov chain Monte-Carlo methods for nonlinear and non-Gaussian state-space models. Comm. Statist. Simulation Comput. 28(4):1999;867-894.
19. Ghysels E., Harvey A.C., Renault E. Stochastic volatility. Maddala G.S., Rao C.R. Handbook of Statistics, Vol. 14. 1996;119-191 North-Holland, Amsterdam.
20. Goffe W.L., Ferrier G.D., Rogers J. Global optimization of statistical functions with simulated annealing. J. Econometrics. 60(1&2):1994;65-99.
21. Gordon N.J., Salmond D.J., Smith A.F.M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc.-F. 140(2):1993;107-113.
22. Härdle W. Applied nonparametric regression. 1990;Cambridge University Press, Cambridge.
23. Izenman A.J. Recent developments in nonparametric density estimation. J. Amer. Statist. Assoc. 86(413):1991;205-224.
24. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P., 1983. Optimization by simulated annealing. Science 220, 4598, 671-680.
25. Kitagawa, G., 1987. Non-Gaussian state-space modeling of nonstationary time series. J. Amer. Statist. Assoc. 82, 1032-1063 (with discussion).
26. Kitagawa G. Monte Carlo filter and smoother for non-Gaussian nonlinear state-space models. J. Comput. Graphical Statist. 5(1):1996;1-25.
27. Kitagawa G. A self-organizing state-space model. J. Amer. Statist. Assoc. 93(443):1998;1203-1215.
28. Kitagawa G., Gersch W. Smoothness priors analysis of time series. Lecture Notes in Statistics. Vol. 116:1996;Springer, Berlin.
29. Kramer S.C., Sorenson H.W. Recursive Bayesian estimation using piece-wise constant approximations. Automatica. 24(6):1988;789-801.
30. O'Hagan, A., 1994, Kendall's Advanced Theory of Statistics, Vol. 2B (Bayesian Inference). Edward Arnold, Paris.
31. Prakasa Rao B.L.S. Nonparametric functional estimation. 1983;Academic Press, New York.
32. Silverman, B.W., 1986. Density estimation for statistics and data analysis, Monographs on Statistics and Applied Probability, Vol. 26, Chapman & Hall, London.
33. Smith A.F.M., Roberts G.O. Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B. 55(1):1993;3-23.
34. Tanizaki, H., 1993. Nonlinear Filters: Estimation and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 400, Springer, Berlin.
35. Tanizaki H. Nonlinear Filters: Estimation and Applications. (Second, Revised and Enlarged Edition). 1996;Springer, Berlin.
36. Tanizaki H. On nonlinear and nonnormal filter using rejection sampling. IEEE Trans. Automat. Control. 44(2):1999;314-319.
37. Tanizaki, H., 2000. Nonlinear and non-Gaussian state-space modeling with Monte Carlo techniques: a survey and comparative study. In: Rao, C.R., Shanbhag, D.N. (Eds.), Handbook of Statistics (Stochastic Processes: Modeling and Simulation). North-Holland, Amsterdam, forthcoming.
38. Tanizaki, H., Mariano, R.S., 1994. Prediction, filtering and smoothing in nonlinear and nonnormal cases using Monte-Carlo integration. J. Appl. Econometrics 9(2), 163-179. Tanizaki, H., Mariano, R.S. In: van DijK, H.K., Manfort, A., Brown, B.W. (Eds.), Econometric Inference Using Simulation Techniques, Wiley, New York, pp. 245-261 (Chapter 12).
39. Tanizaki, H., Mariano, R.S., 1994. Prediction, filtering and smoothing in nonlinear and nonnormal cases using Monte-Carlo integration. J. Appl. Econometrics 9(2), 163-179. Tanizaki, H., Mariano, R.S. In: van DijK, H.K., Manfort, A., Brown, B.W. (Eds.), Econometric Inference Using Simulation Techniques, Wiley, New York, pp. 245-261 (Chapter 12).
40. Tanizaki H., Mariano R.S. Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations. J. Econometrics. 83(1,2):1998;263-290.
41. Tanner M.A. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions. 1993;Springer, Berlin.
42. Tanner, M.A., Wong, W.H., 1987. The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 (398), 528-550 (with discussion).
43. Tierney L. Markov Chains for exploring posterior distributions. Ann. Statist. 22(4):1994;1701-1762.
44. Ullah A. Non-parametric estimation of econometric functionals. Canad. J. Econom. 21(3):1988;625-658.
45. Wei G.C.G., Tanner M.A. A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Amer. Statist. Assoc. 85(411):1990;699-704.