论文信息 - Density estimation by wavelet thresholding

Density estimation by wavelet thresholding

Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients. Minimax rates of convergence are studied over a large range of Besov function classes B σpq and for a range of global L' p error measures, 1 ≤ p' p, some form of nonlinearity is essential, since the minimax linear estimators are suboptimal by polynomial powers of n. A second approach, using an approximation of a Gaussian white-noise model in a Mallows metric, is used to attain exactly optimal rates of convergence for quadratic error (p' = 2).

I. Johnstone | D. Donoho | G. Kerkyacharian | D. Picard

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