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B0525
Title: Hybrid estimators for discretely observed small diffusion processes Authors:  Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: We consider parametric inference for both drift and volatility parameters of small diffusion processes based on high frequency data. The adaptive maximum likelihood (ML) type estimator and the adaptive Bayes type estimator are proposed. By using the polynomial type large deviation inequality for the statistical random field and the Ibragimov-Has'minskii-Kutoyants program recursively, it is proved that the estimators have asymptotic normality and convergence of moments as the sample size tends to infinity and the small dispersion parameter goes to zero. Furthermore, we study the hybrid estimator defined by the adaptive ML type estimation with the initial Bayes type estimator and show that the estimator has asymptotic normality and convergence of moments. In order to investigate the asymptotic behavior of the estimators from the viewpoint of numerical analysis, we give an example and simulation results for the adaptive estimator and the hybrid estimator. This is a joint work with Ryosuke Nomura.