Nonlinear and nonnormal filters are introduced and developed. Traditional nonlinear filters such as the extended Kalman filter and the Gaussian sum filter give biased filtering estimates, and therefore several nonlinear and nonnormal filters have been derived from the underlying probability density functions. The density-based nonlinear filters introduced in this book utilize numerical integration, Monte-Carlo integration with importance sampling or rejection sampling and the obtained filtering estimates are asymptotically unbiased and efficient. By Monte-Carlo simulation studies, all the nonlinear filters are compared. Finally, as an empirical application, consumption functions based on the rational expectation model are estimated for the nonlinear filters, where US, UK and Japan economies are compared.
Reflecting current technological capacities and analytical trends, Computational Methods in Statistics and Econometrics showcases Monte Carlo and nonparametric statistical methods for models, simulations, analyses, and interpretations of statistical and econometric data. The author explores applications of Monte Carlo methods in Bayesian estimation, state space modeling, and bias correction of ordinary least squares in autoregressive models. The book offers straightforward explanations of mathematical concepts, hundreds of figures and tables, and a range of empirical examples. A CD-ROM packaged with the book contains all of the source codes used in the text.
This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
Tokyo Seven Roses' is set in Japan during the waning months of WWII and the beginning of the Occupation. It is written as a diary kept from April 1945 to April 1946 by Shinsuke Yamanaka, a fifty-three-year-old fan-maker living in Nezu, part of Tokyo's shitamachi (old-town) district. After the war, Shinsuke learns by chance that the Occupation forces are plotting a nefarious scheme: in order to cut Japan off from its dreadful past, they intend to see that the language is written henceforth using the alphabet. To fight off this unheard-of threat to the integrity of Japanese culture, seven beautiful women – the Seven Roses – take a stand.
This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
Nonlinear and nonnormal filters are introduced and developed. Traditional nonlinear filters such as the extended Kalman filter and the Gaussian sum filter give biased filtering estimates, and therefore several nonlinear and nonnormal filters have been derived from the underlying probability density functions. The density-based nonlinear filters introduced in this book utilize numerical integration, Monte-Carlo integration with importance sampling or rejection sampling and the obtained filtering estimates are asymptotically unbiased and efficient. By Monte-Carlo simulation studies, all the nonlinear filters are compared. Finally, as an empirical application, consumption functions based on the rational expectation model are estimated for the nonlinear filters, where US, UK and Japan economies are compared.
Reflecting current technological capacities and analytical trends, Computational Methods in Statistics and Econometrics showcases Monte Carlo and nonparametric statistical methods for models, simulations, analyses, and interpretations of statistical and econometric data. The author explores applications of Monte Carlo methods in Bayesian estimation, state space modeling, and bias correction of ordinary least squares in autoregressive models. The book offers straightforward explanations of mathematical concepts, hundreds of figures and tables, and a range of empirical examples. A CD-ROM packaged with the book contains all of the source codes used in the text.
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