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作者：Giraud, Christophe; Tsybakov, Alexandre
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; ENSAE Paris
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作者：Liu, Han; Han, Fang; Yuan, Ming; Lafferty, John; Wasserman, Larry
作者单位：Princeton University; Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health; University System of Georgia; Georgia Institute of Technology; University of Chicago; Carnegie Mellon University
摘要：We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently and robustly estimating high-dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by Liu, Lafferty and Wasserman [J. Mach. Learn. Res. 10 (2009) 2295-2328]. To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman's rho and Kendall's tau. We prove that the nonparanor...
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作者：Soltanolkotabi, Mahdi; Candes, Emmanuel J.
作者单位：Stanford University
摘要：This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009 (2...
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作者：Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry
作者单位：Carnegie Mellon University; Sapienza University Rome
摘要：We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.
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作者：Asgharian, Masoud; Carone, Marco; Fakoor, Vahid
作者单位：McGill University; University of California System; University of California Berkeley; Ferdowsi University Mashhad
摘要：The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751-761] is an incomplete data problem whereby two independent samples from the lifetime distribution G, X-m = (X-1, ... , X-m) and Z(n) = (Z(1), ... , Z(n)), are observed subject to a form of coarsening. Specifically, sample X-m is fully observed while Y-n = (Y-1, ... , Y-n) is observed instead of Z(n), where Y-i = U(i)Z(i) and (U-1, ... , U-n) is an independent sample from the standard uniform distribution. Vardi [B...
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作者：Cook, R. Dennis; Forzani, Liliana; Rothman, Adam J.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); National University of the Littoral
摘要：We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.
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作者：Johnson, Leif T.; Geyer, Charles J.
作者单位：Alphabet Inc.; Google Incorporated; University of Minnesota System; University of Minnesota Twin Cities
摘要：A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially light. We show how to apply the change-of-variable formula for diffeomorphisms to ob...
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作者：Agarwal, Alekh; Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framework that allows the ambient dimension d to grow with (and possibly exceed) the sample size n. Our theory identifies conditions under which projected gradient descent enjoys globally ...
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作者：Durot, Cecile; Kulikov, Vladimir N.; Lopuhaa, Hendrik P.
作者单位：Delft University of Technology
摘要：Let f be a nonincreasing function defined on [0, 1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between f and its Grenander-type estimator on sub-intervals of [0, 1]. The rate of convergence is found to be of order (n/logn)(-1/3) and the limiting distribution to be Gumbel.
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Levy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time i...
