扩散模型中扩散系数的非参数组合估计

Nonparametric Combining Estimation of the Diffusion Coefficient of Diffusion Models

  • 摘要: 为了提高扩散系数估计的准确度, 我们利用动态组合时间域与状态域信息提出一个新的组合估计量. 我们发现所提组合估计量能有效估计扩散模型的扩散系数, 正如在本文中模拟所示. 在一定的条件下, 建立了估计量的渐进正态性, 并证明了时间域估计量与状态域估计量是渐进独立的. 大量的模拟展示了所提组合估计量优于单域估计量, 也优于本文所提估计量.

     

    Abstract: In order to improve the accuracy of the diffusion coefficient estimation, we propose a new combining estimator to estimate the diffusion coefficient by dynamically integrating information from the time-domain and the state-domain. We find that the proposed estimator can effectively estimate the diffusion coefficient of diffusion models, as we show in this paper on simulated time series. Under certain conditions, the asymptotic normality is separately established for the proposed nonparametric estimators and the proposed theorem proves that the time-domain and state-domain estimators are asymptotically independent. Extensive simulations demonstrate the proposed estimator outperforms the other two estimators, and also outperforms the ones in the literature.

     

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