Deconvolution with Supersmooth Distributions
نویسنده
چکیده
The desire to recover the unknown density when data are contaminated with errors leads to nonparametric deconvolution problems. Optimal global rates of convergence are found under the weighted Lp-loss (1 $ p $ 00). It appears that the optimal rates of convergence are extremely slow for supersmooth error distributions. To overcome the difficulty, we examine how large the noise level can be for deconvolution to be feasible, and for the deconvolution estimate to be as good as the ordinary density estimate. It is shown that if noise level is not too large, nonparametric Gaussian deconvolution can still be practical. Several simulation studies are also presented. oAbbreviated title. Supersmooth Deconvolution. AMS 1980 lubject clallijication. Primary 62G20. Secondary 62G05. Key wortU and phralel. Deconvolution, Fourier transforms, kernel density estimates, Lp-norm, global rates of convergence, minimax risks.
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