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作者：Chernozhukov, Victor; Chetverikov, Denis; Kato, Kengo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
摘要：This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide variety of statistical problems, such as construction of uniform confidence bands for functions. Notably, the bound in the main approximation theorem is nonasymptotic and the theorem allows for functions...
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作者：Kuipers, Jack; Moffa, Giusi; Heckerman, David
作者单位：University of Regensburg; University of Regensburg; Microsoft
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作者：Kong, Efang; Xia, Yingcun
作者单位：University of Kent; National University of Singapore
摘要：Sufficient dimension reduction [J. Amer Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus more efficient. Asymp...
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作者：Dette, Holger; Grigriev, Yuri
作者单位：Ruhr University Bochum; Saint Petersburg State Electrotechnical University
摘要：E-optimal experimental designs for a second-order response surface model with k >= 1 predictors are investigated. If the design space is the k-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132] determined optimal designs in a restricted class of designs (defined by the multiplicity of the minimal eigenvalue) and stated their universal optimality as a conjecture. In this paper, we prove this claim and show that these designs are in fact E-optimal in the cla...
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作者：Evans, Robin J.; Richardson, Thomas S.
作者单位：University of Oxford; University of Washington; University of Washington Seattle
摘要：Acyclic directed mixed graphs (ADMGs) are graphs that contain directed (->) and bidirected (<->) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first...
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作者：Sun, Fasheng; Liu, Min-Qian; Qian, Peter Z. G.
作者单位：Northeast Normal University - China; Northeast Normal University - China; Nankai University; Nankai University; University of Wisconsin System; University of Wisconsin Madison
摘要：Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multifidelity computer models, stochastic optimization problems, multi-level fitting of nonparametric functions, and linking parameters. We propose methods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other a...
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作者：Du, Lilun; Zhang, Chunming
作者单位：University of Wisconsin System; University of Wisconsin Madison; Nankai University
摘要：In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value, (p(1), p(2)), for each hypothesis, where pi is a preliminary p-value from prior information and p(2) is the primary p-value for the ultimate analysis. To fi...
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作者：Maire, Florian; Douc, Randal; Olsson, Jimmy
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Royal Institute of Technology
摘要：In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different 7-reversible Markov transition kernels P and Q. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels Pi and Q(i), i is an element of {0, 1}, as soon as the kernels of each pair (P-0, P-1) and (Q(0), Q(1)) can be ordered in the sense of...
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作者：Yoshimori, Masayo; Lahiri, Partha
作者单位：University of Osaka; University System of Maryland; University of Maryland College Park
摘要：We introduce a new adjusted residual maximum likelihood method (REML) in the context of producing an empirical Bayes (EB) confidence interval for a normal mean, a problem of great interest in different small area applications. Like other rival empirical Bayes confidence intervals such as the well-known parametric bootstrap empirical Bayes method, the proposed interval is second-order correct, that is, the proposed interval has a coverage error of order O(m(-3/2)). Moreover, the proposed interv...
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作者：Buecher, Axel; Segers, Johan; Volgushev, Stanislav
作者单位：Ruhr University Bochum; Universite Catholique Louvain
摘要：In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions equipped with the supremum metric. However, there are cases when weak convergence in those spaces fails to hold. Examples include empirical copula and tail dependence processes and residual empirical processes in linear regression models in case the underlying d...
