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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 Using the Gibbs sampler and the Metropolis-Hastings algorithm, an asymptotically exact estimate of the smoothing mean is obtained from any nonlinear and/or non-Gaussian model. Moreover, taking several… (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 Metropolis-Hastings independence sampling (MH) are utilized. Utilizing the random draws generated from the joint density, the… (More)

SUM M ARY N on-para metric tests that deal with two samples include scores tests (such as the W ilcoxon rank sum test, nor mal scores test, log istic scores test, Cauchy scores test, etc.) and Fisher's random ization test. B ecause the non-p arametric tests generally require a large amount of computational work, there are few studies on small-sample… (More)

In the case of U.S. national accounts, the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper, we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduced and derived from a context of the nonlinear filtering or… (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)

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 α t… (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 esti-mator proposed by Andrews (1993, Econometrica 61 (1), 139 –165)… (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
- 1995

In testing a structural change, the approximated confidence intervals are conventionally used for CUSUM and CUSUMSQ tests. This paper numerically derives the asymptotically exact confidence intervals of CUSUM and CUSUMSQ tests. It can be easily extended to nonnormal and/or nonlinear models.