Abstract
In this paper, we consider possibly misspecified stochastic differential equation models driven by Lévy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, in the misspecified case, the asymptotic distribution of the estimator varies by the correction of the misspecification bias, and consistent estimators for the asymptotic variance proposed in the correctly specified case may lose theoretical validity. As one of its solutions, we propose a bootstrap method for approximating the asymptotic distribution. We show that our bootstrap method theoretically works in both correctly specified case and misspecified case without assuming the precise distribution of the driving noise.
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Acknowledgements
The author would like to thank Professor Y.Koike for his constructive advice on bootstrap weights. He is also grateful to the anonymous referees for their valuable comments.
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This work was supported by JST CREST Grant Number JPMJCR14D7, Japan, and JSPS KAKENHI Grant Number JP19K20230.
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Uehara, Y. Bootstrap method for misspecified ergodic Lévy driven stochastic differential equation models. Ann Inst Stat Math 75, 533–565 (2023). https://doi.org/10.1007/s10463-022-00854-2
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DOI: https://doi.org/10.1007/s10463-022-00854-2