Cm. Hurvich et Cl. Tsai, A CROSSVALIDATORY AIC FOR HARD WAVELET THRESHOLDING IN SPATIALLY ADAPTIVE FUNCTION ESTIMATION, Biometrika, 85(3), 1998, pp. 701-710
We consider the selection of a hard wavelet threshold for recovery of
a signal embedded in additive Gaussian white noise. This is closely re
lated to the problem of selection of a subset model in orthogonal norm
al 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 crossvalid
atory version of AIC which, like universal thresholding and Nason's me
thod, can be implemented in O(n log n) operations, where n is the samp
le size. A simulation study reveals that both of the crossvalidatory m
ethods can outperform universal hard thresholding.