A crossvalidatory AIC for hard wavelet thresholding in spatially adaptive function estimation

We consider the selection of a hard wavelet threshold for recovery of a signal embedded in additive Gaussian white noise. This is closely related to the problem of selection of a subset model in orthogonal normal linear regression. We start with a discussion of Donoho & Johnstone's (1994) universal method. Next, we give a computationally efficient algorithm for implementing a crossvalidatory method proposed by Nason (1996). Then, we propose and develop theory in support of a crossvalidatory version of AIC which, like universal thresholding and Nason's method, can be implemented in O(n log n) operations, where n is the sample size. A simulation study reveals that both of the crossvalidatory methods can outperform universal hard thresholding.