基于强混样本的带偏差密度模型的小波估计

Wavelet density estimation based on biased and strong mixing data

为了解决强混样本下带偏差密度估计问题,基于小波方法构造了线性小波估计器,并在Bp,qs(R)空间中给出了该估计器在积分均方误差意义下的收敛阶。结果表明,当p≥2时,估计器达到最优收敛阶。另外,当样本由强混退回独立时,主要定理与独立情形下的结论相同。

To solve the density estimation problem with biased and strong mixing sample, this paper constructs a linear wavelet estimator by wavelet method, and gives the convergence rate in the sense of mean integrated square error over Bp,qs(R) space. The result shows that the estimator achieves the optimal convergence rate when p≥2. In addition, when strong mixing becomes to independent, our theorem is the same as that of the independence case.