ON MINIMAX WAVELET ESTIMATORS

In the paper minimax rates of convergence for wavelet estimators are s tudied. The estimators are based on the shrinkage of empirical coeffic ients <(beta)over cap>(jk) of wavelet decomposition of unknown functio n 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. Th e constructed estimate is minimax (up to constant) for all L(pi) error measures, 0 < pi less than or equal to infinity simultaneously. (C) 1 996 Academic Press, Inc.