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作者：Brown, LD; Lin, Y
作者单位：University of Pennsylvania
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作者：van de Geer, S
作者单位：Leiden University - Excl LUMC; Leiden University
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作者：Hoffmann, M; Lepski, O
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in L-2-norm. Links to a...
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作者：Salibian-Barrera, M; Zamar, RH
作者单位：University of British Columbia
摘要：We introduce a new computer-intensive method to estimate the distribution of robust regression estimates. The basic idea behind Our method is to bootstrap a reweighted representation of the estimates. To obtain a bootstrap method that is asymptotically correct, we include the auxiliary scale estimate in our reweighted representation of the estimates. Our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations. The weights we use are...
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作者：Juditsky, A; Nemirovski, A
作者单位：Technion Israel Institute of Technology
摘要：We consider the problem of estimating the distance from an unknown signal, observed in a white-noise model, to convex cones of positive/monotone/convex functions. We show that, when the unknown function belongs to a Holder class, the risk of estimating the L-r-distance, 1 less than or equal to r < infinity, from the signal to a cone is essentially the same (up to a logarithmic factor) as that of estimating the signal itself. The same risk bounds hold for the test of positivity, monotonicity an...
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作者：Tsybakov, AB
作者单位：Universite Paris Cite; Sorbonne Universite
