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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 ...
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作者：Castillo, Ismael; Schmidt-Hieber, Johannes; Van der Vaart, Aad
作者单位：Sorbonne Universite; Universite Paris Cite; Leiden University - Excl LUMC; Leiden University
摘要：We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significan...
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作者：Low, Mark G.; Ma, Zongming
作者单位：University of Pennsylvania
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作者：Klopp, Olga; Pensky, Marianna
作者单位：Universite Paris Saclay; State University System of Florida; University of Central Florida
摘要：The objective of the present paper is to develop a minimax theory for the varying coefficient model in a nonasymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time-dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and construct an adapti...
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作者：Levrard, Clement
作者单位：Inria
摘要：Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of O(1/n), where n is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron. J. Stat. 7 (2013) 1716-1746]. This rate is attained for the empirical risk minimizer strategy, if the source distribution satisfies some regularity conditions. However, the dependency of the average distortion on other parameters is not known, and these results are only ...
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作者：Sagnol, Guillaume; Harman, Radoslav
作者单位：Zuse Institute Berlin; Comenius University Bratislava
摘要：Let the design of an experiment be represented by an s-dimensional vector w of weights with nonnegative components. Let the quality of w for the estimation of the parameters of the statistical model be measured by the criterion of D-optimality, defined as the mth root of the determinant of the information matrix M(w) = Sigma(s)(i=1) w(i)A(i)A(i)(T), where A(i), i = 1, ... , s are known matrices with in rows. In this paper, we show that the criterion of D-optimality is second-order cone represe...
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作者：Hu, Linwei; Yang, Min; Stufken, John
作者单位：University System of Georgia; University of Georgia; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Arizona State University; Arizona State University-Tempe
摘要：We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stuficen [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and...
