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作者：Juditsky, Anatoli; Nemirovski, Arkadi
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University System of Georgia; Georgia Institute of Technology
摘要：We consider the problem of recovering linear image Bx of a signal x known to belong to a given convex compact set chi from indirect observation omega = Ax + sigma xi of x corrupted by Gaussian noise xi. It is shown that under some assumptions on chi (satisfied, e.g., when chi is the intersection of K concentric ellipsoids/elliptic cylinders), an easy-to-compute linear estimate is near-optimal in terms of its worst case, over x is an element of chi, expected parallel to.parallel to(2)(2)-loss. ...
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作者：Gregory, Karl B.; Lahiri, Soumendra N.; Nordman, Daniel J.
作者单位：University of South Carolina System; University of South Carolina Columbia; North Carolina State University; Iowa State University
摘要：Quantile regression allows for broad (conditional) characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications. Because quantile regression estimators have complex limiting distributions, several bootstrap methods for the independent data setting have been proposed, many of which involve smoothing steps to improve bootstrap approximations. Currently, no similar advances in smoothed bootstraps exist for quantile regr...
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作者：Nandy, Preetam; Hauser, Alain; Maathuis, Marloes H.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Main approaches for learning Bayesian networks can be classified as constraint-based, score-based or hybrid methods. Although high-dimensional consistency results are available for constraint-based methods like the PC algorithm, such results have not been proved for score-based or hybrid methods, and most of the hybrid methods have not even shown to be consistent in the classical setting where the number of variables remains fixed and the sample size tends to infinity. In this paper, we show t...
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作者：Pennec, Xavier
作者单位：Universite Cote d'Azur; Inria
摘要：This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of k+1 reference points. As this definition relies on points and not on tangent vectors, it can also be extended to geodesic spaces which are not Riemannian. For instance, in stratified spaces, it natural...
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作者：Zhu, Liping; Zhang, Yaowu; Xu, Kai
作者单位：Renmin University of China; Shanghai University of Finance & Economics; Shanghai University of Finance & Economics
摘要：In this article, we introduce the notion of interval quantile independence which generalizes the notions of statistical independence and quantile independence. We suggest an index to measure and test departure from interval quantile independence. The proposed index is invariant to monotone transformations, nonnegative and equals zero if and only if the interval quantile independence holds true. We suggest a moment estimate to implement the test. The resultant estimator is root-n-consistent if ...
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作者：Butucea, Cristina; Ndaoud, Mohamed; Stepanova, Natalia A.; Tsybakov, Alexandre B.
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; ENSAE Paris; Carleton University
摘要：We derive nonasymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model in R-d for classes of at most s-sparse vectors separated from 0 by a constant a > 0. In some cases, we get exact expressions for the nonasymptotic minimax risk as a function of d, s, a and find explicitly the minimax selectors. These results are extended to dependent or non-Gaussian observations and to the problem of crowdsourcing. Analogous conclusions are obtained ...
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作者：Han, Kyunghee; Park, Byeong U.
作者单位：Seoul National University (SNU)
摘要：In this work, we develop a new smooth backfitting method and theory for estimating additive nonparametric regression models when the covariates are contaminated by measurement errors. For this, we devise a new kernel function that suitably deconvolutes the bias due to measurement errors as well as renders a projection interpretation to the resulting estimator in the space of additive functions. The deconvolution property and the projection interpretation are essential for a successful solution...
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作者：Zhao, Tuo; Liu, Han; Zhang, Tong
作者单位：University System of Georgia; Georgia Institute of Technology; Princeton University; Tencent
摘要：The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: warm start initialization, active set updating and strong rule for coordinate preselection. Such a complex algorithmic structure grants superior empirical performance, but also poses significant challenge to theoretical analysis. To tackle this lo...
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作者：Li, Jialiang; Jin, Baisuo
作者单位：National University of Singapore; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：A two-stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerated failure time (AFT) model is developed in this paper. In the first stage, we formulate the threshold problem as a group model selection problem so that a concave 2-norm group selection method can be applied. In the second stage, the thresholds are finalized via a refining method. We establish the strong consistency of the threshold estimates and regression coefficien...
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作者：Proksch, Katharina; Werner, Frank; Munk, Axel
作者单位：University of Gottingen; Max Planck Society
摘要：In this paper, we propose a multiscale scanning method to determine active components of a quantity f w.r.t. a dictionary U from observations Y in an inverse regression model Y = T f + xi with linear operator T and general random error xi. To this end, we provide uniform confidence statements for the coefficients , phi is an element of U, under the assumption that (T*)(-1)(U) is of wavelet-type. Based on this, we obtain a multiple test that allows to identify the active components of U, that i...
