Wavelet shrinkage using cross-validation

Wavelets are orthonormal basis functions with special properties that show potential in many areas of mathematics and statistics. This paper concentrates on the estimation of functions and images from noisy data by using wavelet shrinkage. A modified form of twofold cross-validation is introduced to choose a threshold for wavelet shrinkage estimators operating on data sets of length a power of 2. The cross-validation algorithm is then extended to data sets of any length and to multidimensional data sets. The algorithms are compared with established threshold choosers by using simulation. An application to a real data set arising from anaesthesia is presented.