大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Semi-parametric Maximum-Likelihood Estimation for Diffusion Processes

金谷信（Wisconsin-Madison大学経済学部）

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4. Semi-parametric Maximum-Likelihood Estimation for Diffusion Processes

大阪大学 金融・保険セミナーシリーズ 第7回

Semi-parametric Maximum-Likelihood Estimation for Diffusion Processes

金谷信（Wisconsin-Madison大学経済学部）

In this paper, we consider semi-parametric estimation of ergodic diffusion processes, where the drift function is specified parametrically and the diffusion function is unknown. We propose a two-stage estimationstrategy. In the first stage, we estimate the diffusion function, based on the nonparametric kernel method. We derive a new uniform convergence result for the nonparametric estimators over the real line, introducing a new technical device, called a damping function. The uniform convergence result of the nonparametric estimators is used to derive the asymptotic properties for the estimator of the parametric drift function in the second stage, where a semi-parametric log-likelihood is constructed by means of Girsanov theorem. Given a discretely recorded sample with the infill and long-span assumptions, we show that the proposed estimator has root-T consistency with an asymptotically normal distribution under fairly weak conditions, and that its asymptotic variance attains the Cramer-Rao bound.