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作者：Jacod, Jean; Reiss, Markus
作者单位：Universite Paris Cite; Sorbonne Universite; Humboldt University of Berlin
摘要：The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous Ito semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the jumps are not summable In this paper, we study this optimal rate, in the minimax sense and for appropriate bounded nonparametric classes of semimartingales. We show that, if the rth powers of the jumps are sununable for some r is an element of [0, 2), the minimax r...
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作者：Soltanolkotabi, Mahdi; Elhamifar, Ehsan; Candes, Emmanuel J.
作者单位：Stanford University; University of California System; University of California Berkeley; Stanford University
摘要：Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-2797] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the ...
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作者：Fithian, William; Hastie, Trevor
作者单位：Stanford University
摘要：For classification problems with significant class imbalance, subsampling can reduce computational costs at the price of inflated variance in estimating model parameters. We propose a method for subsampling efficiently for logistic regression by adjusting the class balance locally in feature space via an accept reject scheme. Our method generalizes standard case-control sampling, using a pilot estimate to preferentially select examples, whose, responses are conditionally rare given their featu...
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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：Wasserman, Larry
作者单位：Carnegie Mellon University
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作者：He, Xu; Qian, Peter Z. G.
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Wisconsin System; University of Wisconsin Madison
摘要：Orthogonal array based space-filling designs (Owen [Statist. Sinica 2(1992a) 439-452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392-1397]) have become popular in computer experiments, numerical integration, stochastic optimization and uncertainty quantification. As improvements of ordinary Latin hypercube designs, these designs achieve stratification in multi-dimensions. If the underlying orthogonal array has strength t, such designs achieve uniformity up to t dimensions. Existing central lim...
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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...
