Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations

Deck, Thomas

doi:10.1016/j.jmva.2005.04.003

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…From the mathematical viewpoint the basic statistical properties of an estimator (such as consistency, cf. [13]) have to be investigated. From the numerical viewpoint the algorithm has to be tested further and it needs to be improved, in particular for higher-dimensional parameter estimation problems.…”

Section: Final Remarksmentioning

confidence: 99%

Robust Parameter Estimation for Stochastic Differential Equations

Deck

Theting

2004

Acta Appl Math

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We consider the estimation of parameters in stochastic differential equations (SDEs). The problem is treated in the setting of nonlinear filtering theory with a degenerate diffusion matrix. A robust stochastic Feynman-Kac representation for solutions of SDEs of Zakai-type is derived. It is verified that these solutions are conditional densities for the conditional measures defined by degenerate filtering problems. We show that the corresponding estimator for the parameters is robust in the following sense: It depends continuously on both the measurement path and on the intensity of the measurement noise. An algorithm based on a Monte-Carlo approach is given for the practical application of the estimator, and numerical results are reported. Mathematics Subject Classifications (2000): Primary: 62M05, 62M20; secondary: 62F15.

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Section: Final Remarksmentioning

confidence: 99%

Robust Parameter Estimation for Stochastic Differential Equations

Deck

Theting

2004

Acta Appl Math

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“…Nevertheless, in most cases, parameters are always unknown. Over the past few decades, many authors have studied the parameter estimation problem by maximum likelihood estimation [3][4][5], least squares estimation [6][7][8], and Bayes estimation [9,10]. However, non-Gaussian noise such as α-stable noise can more accurately reflect the practical random perturbation.…”

Section: Introductionmentioning

confidence: 99%

Estimation for the Discretely Observed Cox–Ingersoll–Ross Model Driven by Small Symmetrical Stable Noises

Wei

2020

Symmetry

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This paper is concerned with the least squares estimation of drift parameters for the Cox–Ingersoll–Ross (CIR) model driven by small symmetrical α-stable noises from discrete observations. The contrast function is introduced to obtain the explicit formula of the estimators and the error of estimation is given. The consistency and the rate of convergence of the estimators are proved. The asymptotic distribution of the estimators is studied as well. Finally, some numerical calculus examples and simulations are given.

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