In Babenko and Belitser (2010), a new notion for the posterior concentration rate is proposed, the so-called oracle risk rate, the best possible rate over an appropriately chosen estimators family, which is a local quantity (as compared, e.g., with global minimax rates). The program of oracle...

We consider the problem of Bayes estimation of a linear functional of the signal in the Gaussian white noise mode, under the assumption that the unknown signal is from a Sobolev smoothness class. We propose a family of conjugate (Gaussian) priors and prove that the resulting Bayes estimators are...

We consider the median regression model Xk = θ(xk) + ξk, where the unknown signal θ: [0,1] → ℝ, is assumed to belong to a Hölder smoothness class, the ξks are independent, but not necessarily identically distributed, noises with zero median. The distribution of the noise is assumed to...

Summary We consider the median regression model X k = θ( x k ) + ξ k , where the unknown signal θ : [0,1] → ℝ, is assumed to belong to a Hölder smoothness class, the ξ k s are independent, but not necessarily identically distributed, noises with zero median. The distribution of the...