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作者：Donoho, David; Gavish, Matan
作者单位：Stanford University
摘要：An unknown m by n matrix X-0 is to be estimated from noisy measurements Y = X-0 + Z, where the noise matrix Z has i.i.d. Gaussian entries. A popular matrix denoising scheme solves the nuclear norm penalization problem min(X) parallel to Y - X parallel to(2)(F)/2 + lambda parallel to X parallel to* where parallel to X parallel to(*) denotes the nuclear norm (sum of singular values). This is the analog, for matrices, of l(1) penalization in the vector case. It has been empirically observed that ...
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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：Pomatto, Luciano; Al-Najjar, Nabil; Sandroni, Alvaro
作者单位：Northwestern University
摘要：We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the litera...
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作者：McElroy, Tucker S.; Holan, Scott H.
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovariance matrix. We also provide a comprehensive treatment of the asymptotic theory for two-dimensional rand...
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作者：Fryzlewicz, Piotr
作者单位：University of London; London School Economics & Political Science
摘要：We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of localisation, WBS does not re...
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作者：Liu, Weidong; Shao, Qi-Man
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; Chinese University of Hong Kong
摘要：Applying the Benjamini and Hochberg (B H) method to multiple Student's t tests is a popular technique for gene selection in microarray data analysis. Given the nonnormality of the population, the true p-values of the hypothesis tests are typically unknown. Hence it is common to use the standard normal distribution N(0, 1), Student's t distribution t(n-1) or the bootstrap method to estimate the p-values. In this paper, we prove that when the population has the finite 4th moment and the dimensio...
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作者：Fan, Jianqing; Ke, Zheng Tracy
作者单位：Princeton University
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作者：Onatski, Alexei; Moreira, Marcelo J.; Hallin, Marc
作者单位：University of Cambridge; Getulio Vargas Foundation; Universite Libre de Bruxelles; Princeton University
摘要：This paper applies Le Cam's asymptotic theory of statistical experiments to the signal detection problem in high dimension. We consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the Gaussian asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. Those asymptotic p...
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作者：Buehlmann, Peter; Peters, Jonas; Ernest, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structur...
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作者：Ke, Zheng Tracy; Jin, Jiashun; Fan, Jianqing
作者单位：University of Chicago; Carnegie Mellon University; Princeton University
摘要：Consider a linear model Y = X beta +z, where X = X-n,X-p and z similar to N(0, In). The vector beta is unknown but is sparse in the sense that most of its coordinates are 0. The main interest is to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya [In Change-Point Problems (South Had...
