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作者：Gao, Chao; Lu, Yu; Zhou, Harrison H.
作者单位：Yale University
摘要：Network analysis is becoming one of the most active research areas in statistics Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clusters, we show that the optimal rate under the mean squared error is n(-1) log k + k(2)/n(2). The mini...
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作者：Delattre, Sylvain; Roquain, Etienne
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：The false discovery proportion (FDP) is a convenient way to account for false positives when a large number m of tests are performed simultaneously. Romano and Wolf [Ann. Statist. 35 (2007) 1378-1408] have proposed a general principle that builds FDP controlling procedures from k-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [J. Statist. Plann. Inference 124 (2004) 379-398]; Romano and Wolf (2007). However, the theoreti...
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作者：Lepski, Oleg
作者单位：Aix-Marseille Universite
摘要：We address the problem of adaptive minimax estimation in white Gaussian noise models under L-p-loss, 1 <= p <= infinity, on the anisotropic Nikol'skii classes. We present the estimation procedure based on a new data-driven selection scheme from the family of kernel estimators with varying bandwidths. For the proposed estimator we establish so-called L-p-norm oracle inequality and use it for deriving minimax adaptive results. We prove the existence of rate-adaptive estimators and fully characte...
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作者：Chauvet, Guillaume
作者单位：Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：Multistage sampling is commonly used for household surveys when there exists no sampling frame, or when the population is scattered over a wide area. Multistage sampling usually introduces a complex dependence in the selection of the final units, which makes asymptotic results quite difficult to prove. In this work, we consider multistage sampling with simple random without replacement sampling at the first stage, and with an arbitrary sampling design for further stages. We consider coupling m...
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作者：Jirak, Moritz
作者单位：Humboldt University of Berlin
摘要：Consider d dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size n and d tend to infinity. We achieve this either by a consistent bootstrap or an appropriate limit distribution. This allows for the construction of simultaneous confidence bands for dependent change point tests, and explicitly allows us to determine the location of the change both in time and coordina...
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作者：Rousseau, Judith
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
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作者：Li, Jian; Siegmund, David
作者单位：Stanford University
摘要：This paper compares the higher criticism statistic (Donoho and Jin [Ann. Statist. 32 (2004) 962-994]), a modification of the higher criticism statistic also suggested by Donoho and Jin, and two statistics of the Berk Jones [Z Wahrsch. Verw. Gebiete 47 (1979) 47-59] type. New approximations to the significance levels of the statistics are derived, and their accuracy is studied by simulations. By numerical examples it is shown that over a broad range of sample sizes the Berk Jones statistics hav...
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作者：Ren, Zhao; Sun, Tingni; Zhang, Cun-Hui; Zhou, Harrison H.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University System of Maryland; University of Maryland College Park; Rutgers University System; Rutgers University New Brunswick; Yale University
摘要：The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition rela...
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作者：Castillo, Ismael; Rousseau, Judith
作者单位：Sorbonne Universite; Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
摘要：A Bernstein-von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle semiparametric bias, in particular for nonlinear functionals and in cases where regularity is possibly low. Examples include the squared L-2-norm in Gaussian white noise, nonlinear functionals in density estimation, as well as functionals in autoregressive models. For ...
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作者：Barber, Rina Foygel; Candes, Emmanuel J.
作者单位：University of Chicago; Stanford University
摘要：In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR) the expected fraction of false discoveries among all discoveries is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff ...
