## On minimax wavelet estimators.(English)Zbl 0865.62023

Summary: Minimax rates of convergence for wavelet estimators are studied. The estimators are based on the shrinkage of empirical coefficients $$\widehat\beta_{jk}$$ of wavelet decompositions of unknown functions with thresholds $$\lambda_j$$. These thresholds depend on the regularity of the function to be estimated. In the problem of density estimation and nonparametric regression we establish upper rates of convergence over a large range of functional classes and global error measures. The constructed estimate is minimax (up to constant) for all $$L_\pi$$ error measures, $$0<\pi\leq\infty$$, simultaneously.

### MSC:

 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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