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作者：Gassiat, Elisabeth; Le Corff, Sylvain; Lehericy, Luc
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on observations of the corrupted signal. We establish the identifiability of the model up to translation when the signal has a Laplace transform with an exponential growth rho small...
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作者：Kuchibhotla, Arun K.; Patra, Rohit K.
作者单位：Carnegie Mellon University; State University System of Florida; University of Florida
摘要：We consider least squares estimation in a general nonparametric regression model where the error is allowed to depend on the covariates. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the error has a uniformly bounded conditional variance and has only finitely many moments. Our upper bound on the rate of convergence of the LSE depe...
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作者：Fan, Zhou
作者单位：Yale University
摘要：Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational invariance in law,...
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作者：Ghosh, Swarnadip; Hastie, Trevor; Owen, Art B.
作者单位：Stanford University
摘要：Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as N-3/2 (or worse) for N observations. Papaspiliopoulos, Roberts and Zanella (Biometrika 107 (2020) 25-40) present a collapsed Gibbs sampler that costs O(N), but under an extremely stringent sampling model. We propose a backfitting algorithm to compute a generalized least squares estimate and prove that it costs O(N). A critical pa...
