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作者：Anandkumar, Animashree; Tan, Vincent Y. F.; Huang, Furong; Willsky, Alan S.
作者单位：National University of Singapore; Agency for Science Technology & Research (A*STAR); A*STAR - Institute for Infocomm Research (I2R)
摘要：We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of n = Omega(J(min)(-2) log p), where ...
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作者：Li, Gaorong; Peng, Heng; Zhang, Jun; Zhu, Lixing
作者单位：Beijing University of Technology; Hong Kong Baptist University; Shenzhen University
摘要：Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or large p, small n paradigms when p can be as large as an exponential of the sample size n. In this paper we propose a robust rank correlation screening (RRCS) method to deal with ultra-high dimensional data. The new procedure is based on the Kendall tau correlation coefficient between response and predictor ...
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作者：Xue, Lingzhou; Zou, Hui; Cai, Tianxi
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Harvard University
摘要：The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an approach is computati...
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作者：Pillai, Natesh S.; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：Let (X) over tilde (MxN) be a rectangular data matrix with independent real-valued entries [(x) over tilde (ij)] satisfying E (x) over tilde (ij) = 0 and E (x) over tilde (2)(ij) = 1/M, N, M -> infinity. These entries have a subexponential decay at the tails. We will be working in the regime N/M = d(N), lim(N ->infinity) d(N) not equal 0, 1, infinity. In this paper we prove the edge universality of correlation matrices X-dagger X, where the rectangular matrix X (called the standardized matrix)...
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作者：Foygel, Rina; Draisma, Jan; Drton, Mathias
作者单位：University of Chicago; Eindhoven University of Technology
摘要：A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation m...
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作者：Tchetgen, Eric J. Tchetgen; Shpitser, Ilya
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard T.H. Chan School of Public Health
摘要：While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon evaluating the total effect of the exposure, investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure, through a mediator...
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作者：Einmahl, John H. J.; Krajina, Andrea; Segers, Johan
作者单位：Tilburg University; University of Gottingen; Universite Catholique Louvain
摘要：Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consist...
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作者：Wu, Yuan; Zhang, Ying
作者单位：University of California System; University of California San Diego; University of Iowa
摘要：The analysis of the joint cumulative distribution function (CDF) with bivariate event time data is a challenging problem both theoretically and numerically. This paper develops a tensor spline-based sieve maximum likelihood estimation method to estimate the joint CDF with bivariate current status data. The I-splines are used to approximate the joint CDF in order to simplify the numerical computation of a constrained maximum likelihood estimation problem. The generalized gradient projection alg...
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作者：Portnoy, Stephen
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Traditionally, assessing the accuracy of inference based on regression quantiles has relied on the Bahadur representation. This provides an error of order n(-1/4) in normal approximations, and suggests that inference based on regression quantiles may not be as reliable as that based on other (smoother) approaches, whose errors are generally of order n(-1/2) (or better in special symmetric cases). Fortunately, extensive simulations and empirical applications show that inference for regression q...
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作者：Rivoirard, Vincent; Rousseau, Judith
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：In this paper, we study the asymptotic posterior distribution of linear functionals of the density by deriving general conditions to obtain a semiparametric version of the Bernstein-von Mises theorem. The special case of the cumulative distributive function, evaluated at a specific point, is widely considered. In particular, we show that for infinite-dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional can be either Gaussian...
