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作者：Daudel, Kamelia; Douc, Randal; Portier, Francois
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：This paper introduces the (alpha, Gamma)-descent, an iterative algorithm which operates on measures and performs alpha-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions Gamma, this algorithm leads at each step to a systematic decrease in the alpha-divergence and derive convergence results. Our fra...
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作者：Mure, Joseph
作者单位：Electricite de France (EDF); Universite Paris Cite
摘要：In a seminal article, Berger, De Oliveira and Sanso [J. Amer. Statist. Assoc. 96 (2001) 1361-1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper posterior. They prove this result for rough correlation kernels: Spherical, Exponential with power rho < 2, Matern with smoothness nu < 1. This paper provides a proof for smooth ...
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作者：Neykov, Matey; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We consider the problem of conditional independence testing of X and Y given Z where X, Y and Z are three real random variables and Z is continuous. We focus on two main cases-when X and Y are both discrete, and when X and Y are both continuous. In view of recent results on conditional independence testing [Ann. Statist. 48 (2020) 1514-1538], one cannot hope to design nontrivial tests, which control the type I error for all absolutely continuous conditionally independent distributions, while s...
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作者：Savje, Fredrik; Aronow, Peter M.; Hudgens, Michael G.
作者单位：Yale University; Yale University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We investigate large-sample properties of treatment effect estimators under unknown interference in randomized experiments. The inferential target is a generalization of the average treatment effect estimand that marginalizes over potential spillover effects. We show that estimators commonly used to estimate treatment effects under no interference are consistent for the generalized estimand for several common experimental designs under limited but otherwise arbitrary and unknown interference. ...
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作者：Jeon, Jeong Min; Park, Byeong U.; Van Keilegom, Ingrid
作者单位：KU Leuven; Seoul National University (SNU)
摘要：Additive regression is studied in a very general setting where both the response and predictors are allowed to be non-Euclidean. The response takes values in a general separable Hilbert space, whereas the predictors take values in general semimetric spaces, which covers a very wide range of nonstandard response variables and predictors. A general framework of estimating additive models is presented for semimetric space-valued predictors. In particular, full details of implementation and the co...
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作者：Kulaitis, Gytis; Munk, Axel; Werner, Frank
作者单位：University of Gottingen; University of Wurzburg
摘要：As a general rule of thumb the resolution of a light microscope (i.e., the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)-the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well-known Abbe and Rayleigh criteria, dating back to the end of the 19th century. However, during the last two decades convent...
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作者：De Castro, Y.; Gadat, S.; Marteau, C.; Maugis-Rabusseau, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：This paper investigates the statistical estimation of a discrete mixing measure mu(0) involved in a kernel mixture model. Using some recent advances in l(1)-regularization over the space of measures, we introduce a data fitting and regularization convex program for estimating mu(0) in a grid-less manner from a sample of mixture law, this method is referred to as Beurling-LASSO. Our contribution is two-fold: we derive a lower bound on the bandwidth of our data fitting term depending only on the...
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作者：Fan, Jianqing; Wang, Weichen; Zhu, Ziwei
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from subexponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Theta* from the trace regression model Y = Tr(Theta* inverted perpendicular(X)) + epsilon. It encompasses four popul...
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作者：Chen, Song Xi; Peng, Liuhua
作者单位：Peking University; Peking University; University of Melbourne
摘要：This paper considers distributed statistical inference for general symmetric statistics in the context of massive data with efficient computation. Estimation efficiency and asymptotic distributions of the distributed statistics are provided, which reveal different results between the nondegenerate and degenerate cases, and show the number of the data subsets plays an important role. Two distributed bootstrap methods are proposed and analyzed to approximation the underlying distribution of the ...
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作者：Comminges, L.; Collier, O.; Ndaoud, M.; Tsybakov, A. B.
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：For the sparse vector model, we consider estimation of the target vector, of its l(2)-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet noise level-noise distribution-sparsity. We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minim...
