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In this paper, an attempt is made to show a general solution to nonlinear and/or non-Gaussian state space modeling in a Bayesian framework, which corresponds to an extension of Carlin, Polson and Stoffer (1992) and Carter and Kohn (1994, 1996). Using the Gibbs sampler and the Metropolis-Hastings algorithm, an asymptotically exact estimate of the smoothing… (More)

- Hisashi Tanizaki
- 2001

In this paper, the nonlinear non-Gaussian filters and smoothers are proposed using the joint density of the state variables, where the sampling techniques such as rejection sampling (RS), importance resampling (IR) and the MetropolisHastings independence sampling (MH) are utilized. Utilizing the random draws generated from the joint density, the… (More)

- Hisashi Tanizaki
- 2000

It is well known that the ordinary least-squares estimates (OLSE) of autoregressive models are biased in small sample. In this paper, an attempt is made to obtain the unbiased estimates in the sense of median or mean. Using Monte Carlo simulation techniques, we extend the median-unbiased estimator proposed by Andrews (1993, Econometrica 61 (1), 139–165) to… (More)

The nonlinear filters based on Taylor series approximation are broadly used for computational simplicity, even though their filtering estimates are clearly biased. In this paper, first, we analyze what is approximated when we apply the expanded nonlinear functions to the standard linear recursive Kalman filter algorithm. Next, since the state variables αt… (More)

Non-parametric tests that deal with two samples include scores tests (such as the Wilcoxon rank sum test, normal scores test, log istic scores test, Cauchy scores test, etc.) and Fisher’s randomization test. B ecause the non-parametric tests generally require a large amount of computational work, there are few studies on small-sample properties, although… (More)

In this paper, a nonlinear and/or non-Gaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the state-space model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random… (More)

- Hisashi Tanizaki
- 2000

Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or non-Gaussian state estimation problems have been developed. Numerical integration becomes extremely computer-intensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling… (More)

- Hisashi Tanizaki
- IEEE Trans. Automat. Contr.
- 1999

In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the state-vector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws are recursively generated at each time. The Monte Carlo… (More)

- Hisashi Tanizaki
- 2000

In the case where the lagged dependent variables are included in the regression model, it is known that the ordinary least squares estimates (OLSE) are biased in small sample and that bias increases as the number of the irrelevant variables increases. In this paper, based on the bootstrap methods, an attempt is made to obtain the unbiased estimates in… (More)

- Hisashi Tanizaki
- 2001

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… (More)