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Statistical deconvolution problems with Fourier-oscillating error densities

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Many problems in nonparametric statistics require the application of deconvolution procedures, e.g. density estimation based on contaminated data, errors-in-variables problems in nonparametric regression, image deblurring. The current talk focuses on rarely studied types of error densities whose Fourier transforms have some zeros and show oscillatory behaviour. New methods are introduced for those deconvolution problems. The optimal convergence rates are derived in several settings. The finite-sample performance is studied by numerical simulations.

This talk is part of the Statistics series.

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