Abstract
We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators in order to select proper initial values for optimisation of the quasi likelihood function. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators are shown, and a concrete example and the simulation results are given.
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Acknowledgements
The authors would like to thank the editor, the associate editor, and the two reviewers for their valuable comments. This work was partially supported by JST CREST, JSPS KAKENHI Grant Number JP17H01100 and Cooperative Research Program of the Institute of Statistical Mathematics.
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Kaino, Y., Nakakita, S.H. & Uchida, M. Hybrid estimation for ergodic diffusion processes based on noisy discrete observations. Stat Inference Stoch Process 23, 171–198 (2020). https://doi.org/10.1007/s11203-019-09203-2
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DOI: https://doi.org/10.1007/s11203-019-09203-2