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Abstract Wavelets have motivated development of a host of new ideas in nonparametric regression smoothing. Here we apply the too] of exact risk analysis, to understand the small sample behavior of wavelet estimators, and thus to check directly the conclusions suggested by asymptotics. Comparisons between some wavelet bases, and also between hard and soft thresholding, are given from several viewpoints. Our results provide insight as to why the viewpoints and conclusions of Donoho and Johnstone differ from those of Hall and Patil.
Marron et al. (Tue,) studied this question.