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作者：Davezies, Laurent; D'Haultfoeuille, Xavier; Guyonvarch, Yannick
摘要：Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same population. Examples include trade flows between countries or relationships in a network. Separately exchangeable arrays are well suited to multiway clustering, where units sharing the same cluster (e.g., geographical areas or sectors of activity when considering in...
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作者：Lahiri, Soumendra N.
作者单位：Washington University (WUSTL)
摘要：This paper investigates conditions for variable selection consistency of the LASSO in high dimensional regression models and gives necessary and sufficient conditions for the same, potentially allowing the model dimension p to grow arbitrarily fast as a function of the sample size n. These conditions require both upper and lower bounds on the growth rate of the penalty parameter. It turns out that a variant of the irrepresentable Condition (IRC) of (J. Mach. Learn. Res. 7 (2006) 2541-2563), he...
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作者：Duffy, James A.; Kasparis, Ioannis
作者单位：University of Oxford; University of Cyprus
摘要：We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity-what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d = 1/2, and arrays of autoregressive processes with roots drifting slowly towards unity. We first apply the theory to study inference in parametric and nonparametric regression models involving WNPs as covariates. We then use these results to d...
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作者：Hallin, Marc; Del Barrio, Eustasio; Cuesta-Albertos, Juan; Matran, Carlos
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Universidad de Valladolid; Universidad de Valladolid; Universidad de Cantabria
摘要：Unlike the real line, the real space R-d, for d >= 2, is not canonically ordered. As a consequence, such fundamental univariate concepts as quantile and distribution functions and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has been an open problem for more than half a century, generating an abundant literature and motivating, among others, the development of statistical depth and c...
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作者：Bercu, Bernard; Bigot, Jeremie
作者单位：Universite de Bordeaux; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is devoted to the stochastic approximation of entropically regularized-Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal transportation problems can be rewritten as a nonstrongly concave optimisation problem. It allows to implement a Robbins-Monro stochastic algorithm to estimate the Sinkhorn divergence using a sequence of data sampled from one of the two distributions. Our main contribut...
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作者：Liu, Haoyang; Gao, Chao; Samworth, Richard J.
作者单位：University of Chicago; University of Cambridge
摘要：We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for n independent, p-variate Gaussian observations. This rate exhibits a phase transition when the sparsity level is of order root p log log (8n) and has a very delicate dependence on the sample size: in a certain sparsity regime, it involves a triple iterated logarithmic factor in n. Furth...
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作者：Fang, Billy; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We consider the problem of nonparametric regression when the covariate is d dimensional, where d >= 1. In this paper, we introduce and study two non-parametric least squares estimators (LSEs) in this setting-the entirely monotonic LSE and the constrained Hardy-Krause variation LSE. We show that these two LSEs are natural generalizations of univariate isotonic regression and univariate total variation denoising, respectively, to multiple dimensions. We discuss the characterization and computati...
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作者：Lei, Jing
作者单位：Carnegie Mellon University
摘要：Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work, we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in t...
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作者：Delyon, Bernard; Portier, Francois
作者单位：Universite de Rennes; Institut Polytechnique de Paris
摘要：This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a safe heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward the target density; ...
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作者：Howard, Steven R.; Ramdas, Aaditya; McAuliffe, Jon; Sekhon, Jasjeet
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University; Carnegie Mellon University; Yale University
摘要：A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric conditions. We draw connections between the Cramer-Chernoff method for exponential concentration, the law of the iterated logarithm (LIL) and the sequential probability ratio test-our confidence sequences are time-uniform extensions of the first; provide tigh...
