高维小波密度估计器的收敛性

Consistency of D-dimensional Wavelet Estimators

摘要: 为了研究高维Lebesgue可测空间 L _p (R ^d )中估计器的收敛性,利用小波方法,给出估计器在 L _p 范数意义下的相合性. 研究发现:若小波尺度函数 φ紧支且满足条件 S, 则任给 f∈ L _p (R ^d ),1≤ p<∞,有 $\begin{matrix} \lim_{n \to \infty} \end{matrix}$ E‖ f- $\begin{matrix} {\hat{f}}_{n} \end{matrix}$ ‖ _p =0.

Abstract: To investigate estimator’s convergence rate over Lebesgue measurable space L _p (R ^d ), wavelet method was used and consistency under L _p norm was given. The main result is that if wavelet scaling function φ has compact support and satisfies condition S, then for any f∈ L _p (R ^d ),1≤ p<∞, we have $\begin{matrix} \lim_{n \to \infty} \end{matrix}$ E‖ f- $\begin{matrix} {\hat{f}}_{n} \end{matrix}$ ‖ _p =0.