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

• Published in: Journal of statistical planning and inference Vol. 96; no. 2; pp. 301 - 323
• Main Author: Tanizaki, Hisashi
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.07.2001; New York,NY Elsevier Science; Amsterdam
• Subjects: Exact sciences and technology; Inference from stochastic processes; time series analysis; Mathematics; Metropolis–Hastings algorithm; Mode estimation; Monte Carlo optimization; Nonparametric density estimation; Nonparametric inference; Probability and statistics; Sciences and techniques of general use; Simulated annealing; State-space model; Statistics; 62M10; Monte Carlo optimization; Metropolis–Hastings algorithm; Simulated annealing; Mode estimation; Nonparametric density estimation; State-space model; 62M20; Density estimation; Parameter estimation; Error estimation; Non Gaussian system; Optimization method; Non parametric estimation; State space; Stochastic process; Linear model; Optimization; State variable; Measurement equation; Function maximization; Sampling; Likelihood function; Sampling error; Monte Carlo method; Non linear estimation; Filtering; Time series; Metropolis Hastings algorithm; Statistical estimation; State space method; Gibbs sampling; Statistical forecasting; Non linear system; Filter; Non linear model; Variable parameter; Transition; Maximum likelihood; Bayes methods; Autocorrelation
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(00)00218-4

For the last decade, various simulation-based nonlinear and non-Gaussian filters and smoothers have been proposed. In the case where the unknown parameters are included in the nonlinear and non-Gaussian system, however, it is very difficult to estimate the parameters together with the state variables, because the state-space model includes a lot of parameters in general and the simulation-based procedures are subject to the simulation errors or the sampling errors. Therefore, clearly, precise estimates of the parameters cannot be obtained (i.e., the obtained estimates may not be the global optima). In this paper, an attempt is made to estimate the state variables and the unknown parameters simultaneously, where the Monte Carlo optimization procedure is adopted for maximization of the likelihood function.