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We consider rst the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be approximated by the Green's function of a certain linear diierential operator. Furthermore, we propose to use the standard (in applied mathematics and engineering)(More)
We consider a problem of recovering a high-dimensional vector µ observed in white noise, where the unknown vector µ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l 0-type penalties. The penalties are associated with various choices of the prior distributions π n (·) on the number of(More)
SUMMARY We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various(More)
SUMMARY We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed(More)
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