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Stochastic Analysis with Financial ApplicationsStrong Consistency of Bayesian Estimator Under Discrete Observations and Unknown Transition Density

Stochastic Analysis with Financial Applications: Strong Consistency of Bayesian Estimator Under... [We consider the asymptotic behavior of a Bayesian parameter estimation method under discrete stationary observations. We suppose that the transition density of the data is unknown, and therefore we approximate it using a kernel density estimation method applied to the Monte Carlo simulations of approximations of the theoretical random variables generating the observations. In this article, we estimate the error between the theoretical estimator, which assumes the knowledge of the transition density and its approximation which uses the simulation. We prove the strong consistency of the approximated estimator and find the order of the error. Most importantly, we give a parameter tuning result which relates the number of data, the number of time-steps used in the approximation process, the number of the Monte Carlo simulations and the bandwidth size of the kernel density estimation.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Stochastic Analysis with Financial ApplicationsStrong Consistency of Bayesian Estimator Under Discrete Observations and Unknown Transition Density

Part of the Progress in Probability Book Series (volume 65)
Editors: Kohatsu-Higa, Arturo; Privault, Nicolas; Sheu, Shuenn-Jyi
Kohatsu-Higa, Arturo; Vayatis, Nicolas; Yasuda, Kazuhiro
Stochastic Analysis with Financial Applications — Jul 12, 2011
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References (7)

Publisher
Springer Basel
Copyright
© Springer Basel AG 2011
ISBN
978-3-0348-0096-9
Pages
145 –167
DOI
10.1007/978-3-0348-0097-6_10
Publisher site
See Chapter on Publisher Site

Abstract

[We consider the asymptotic behavior of a Bayesian parameter estimation method under discrete stationary observations. We suppose that the transition density of the data is unknown, and therefore we approximate it using a kernel density estimation method applied to the Monte Carlo simulations of approximations of the theoretical random variables generating the observations. In this article, we estimate the error between the theoretical estimator, which assumes the knowledge of the transition density and its approximation which uses the simulation. We prove the strong consistency of the approximated estimator and find the order of the error. Most importantly, we give a parameter tuning result which relates the number of data, the number of time-steps used in the approximation process, the number of the Monte Carlo simulations and the bandwidth size of the kernel density estimation.]

Published: Jul 12, 2011

Keywords: Bayesian inference; strong consistency; discrete observations

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