React Scatterplot Smoothers: Superefficiency through Basis Economy

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On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection (2006, background): “Note that some progress has recently been made concerning confidence sets for the entire parameter vector in high-dimensional models (see, e.g., Beran and Dümbgen 1998; Beran 2000; Baraud 2004).”
Adaptive nonparametric confidence sets (2006, methodology): “They justify Beran [4] and Beran and Dümbgen [5] REACT confidence sets in terms of an honest confidence set over β-regular regression functions f , described in terms of a wavelet expansion.”
All of Statistics: A Concise Course in Statistical Inference (2004, methodology): “See also Beran (2000) and Beran and Dümbgen (1998). An introduction to wavelets is given in Ogden (1997). A more advanced treatment can be found in Härdle et al. (1998). The theory of statistical estimation using wavelets has been developed by many authors, especially David Donoho and Ian Johnstone.”