一类密度函数的线性小波估计

Linear Wavelet Density Estimation for Biased Data

为了给出估计器在L p风险意义下的收敛阶,利用小波方法针对一类含噪声的密度函数,构造了线性小波估计器.特别地,当r≥p时,线性小波估计器构造简单且收敛阶优于非线性估计器.另外,当偏差函数g(x)≡1时,所研究模型对应于不含噪声的情形,得到的收敛阶为最佳收敛阶,从而推广了已有结果.

To obtain Lp risk convergence rate, for a kind of density which has noise data, the linear wavelet estimator is constructed. In particular, when r≥p, the linear wavelets estimator is simple and the convergence rate is better than nonlinear estimator. In addition, when the bias function g （x） ≡1, the model is the case which has no noise, and the convergence rate is optimal and generalizes the result which was gotten.