Wavelet Estimator

Definition

Wavelet estimator is a kind of Series Estimator using wavelet basis. $\hat{f}(t)=\sum _{k=-\infty }^{\infty }{\hat{c}}_k{\varphi }_k(t)+\sum _{j=-\infty }^{\infty }\sum _{k=-\infty }^{\infty }{\hat{d}}_{j,k}{\psi }_{j,k}(t)$ where ${\hat{c}}_k=\frac{1}{n}\sum _{i=1}^n{\varphi }_k(x_i)Y_i$ and ${\hat{d}}_{j,k}=\frac{1}{n}\sum _{i=1}^n{\psi }_{j,k}(x_i)Y_i$

To find a optimal resolution Thresholding is used.