Methods of Block Thresholding Across Multiple Resolution Levels in Adaptive Wavelet Estimation

Blocking methods of thresholding have demonstrated many advantages over term-by-term methods in adaptive wavelet estimation. These blocking methods are resolution-level specific, meaning the coefficients are grouped together only within the same resolution level. Techniques have not yet been proposed for blocking across multiple resolution levels and do not take into consideration varying shapes of blocks for wavelet coefficients. Presently, several methods of block thresholding across multiple resolution levels are described. Various simulation studies analyze the use of these methods among nonparametric functions, including comparisons to other blocking and non-blocking wavelet thresholding methods. The introduction of a this new technique questions when this method will be advantageous over resolution-level specific methods. Another simulation study demonstrates a method of statistically selecting when blocking across resolution levels is beneficial over traditional techniques. Additional analysis will conclude how effective the automated selection method is in both simulation and if put into practice.