DECONVOLUTION WITH UNKNOWN ERROR DISTRIBUTION

By Jan Johannes. 2007

120 citations recorded by the source corpus.

We consider the problem of estimating a density fX using a sample Y1, …, Yn from fY=fX⋆fe, where fe is an unknown density. We assume that an additional sample e1, …, em from fe is observed. Estimators of fX and its derivatives are constructed by using nonparametric estimators of fY and fe and by applying a spectral cut-off in the Fourier domain. We derive the rate of convergence of the estimators in case of a known and unknown error density fe, where it is assumed that fX satisfies a polynomial, logarithmic or general source condition. It is shown that the proposed estimators are asymptotically optimal in a minimax sense in the models with known or unknown error density, if the density fX belongs to a Sobolev space $H_{\mathcal{p}}$ and fe is ordinary smooth or supersmooth.

Subfields: Computer Networks and Communications, Radiology, Nuclear Medicine and Imaging, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/279216ba65b30367bb6622d5507e1918520da05a

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In Computer Networks and Communications

In Radiology, Nuclear Medicine and Imaging

In Statistics and Probability

Citations in the corpus

ON DECONVOLUTION OF DISTRIBUTION FUNCTIONS (2010, background): “The outlined problem is closely related to the density deconvolution problem that has been extensively studied in the literature; see, for example, [4, 5, 13, 18, 24, 27, 28] and references therein.”
A SPECTRAL METHOD FOR DECONVOLVING A DENSITY (2010, background): “In, for instance, Efromovich (1997), Johannes (2009), and Neumann (2007), g is estimated nonparametrically.”