潜周期模型在周期型随机数据的数值微分中的应用研究

Research on Derivative Estimation of Periodic Random Data with Hidden Periodical Model

从统计角度给出了一种周期型随机数据的数值微分的新方法。采用经典求解数值微分的思想,利用潜周期模型拟合离散的周期型随机观测数据,将拟合模型的导数作为随机数据的导数估计。基于随机逼近理论讨论了导数估计的存在惟一性,在对误差性质进行分析的基础上,利用极限理论证明了估计的相合性。

In this paper,a new method of the differentiation of a kind of periodic random data from the viewpoint of statistics was proposed.The observed random data was fit with the hidden periodical model（HPM）,and the derivative of HPM as the estimation of the derivative of the function of the real data was used,which follows the common ideal of interpolating numerical differentiation.The existence and the uniqueness of the estimation based on the theory of random approximation were discussed,and which proved the consistency of the estimation by large sample theory after analyzing the error estimation in detail.