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作者：Mei, Song; Bai, Yu; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：Most high-dimensional estimation methods propose to minimize a cost function (empirical risk) that is a sum of losses associated to each data point (each example). In this paper, we focus on the case of nonconvex losses. Classical empirical process theory implies uniform convergence of the empirical (or sample) risk to the population risk. While under additional assumptions, uniform convergence implies consistency of the resulting M-estimator, it does not ensure that the latter can be computed...
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作者：Cai, T. Tony; Guntuboyina, Adityanand; Wei, Yuting
作者单位：University of Pennsylvania; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function. Both the problem of estimating the support function at a point and that of estimating the whole convex set are studied. For pointwise estimation, we consider the problem in a general nonasymptotic framework, which evaluates the performance of a procedure at each individual set, instead of the worst case performance over a large parameter space as in conventio...
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作者：Lin, Zhenhua; Mueller, Hans-Georg; Yao, Fang
作者单位：University of Toronto; University of California System; University of California Davis; Peking University
摘要：We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied to data in any infinite-dimensional Hilbert space, the case of functional data that are random eleme...
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作者：Bellec, Pierre C.; Lecue, Guillaume; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Rutgers University System; Rutgers University New Brunswick
摘要：We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the minimax prediction and l(2) estimation rate (s/n)log(p/s) in high-dimensional linear regression on the class of s-sparse vectors in R-P. This is done under the Restricted Eigenvalue (RE) condition for the Lasso and under a slightly more constraining assumption on the design for the Slope. The main results have the form of sharp oracle inequalities ac...
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作者：Finner, Helmut; Gontscharuk, Veronika
作者单位：Heinrich Heine University Dusseldorf; Leibniz Association; Deutsches Diabetes-Zentrum (DDZ); Leibniz Association; Deutsches Diabetes-Zentrum (DDZ); Heinrich Heine University Dusseldorf
摘要：From a multiple testing viewpoint, Kolmogorov-Smirnov (KS)-type tests are union-intersection tests which can be redefined in terms of local levels. The local level perspective offers a new viewpoint on ranges of sensitivity of KS-type tests and the design of new tests. We study the finite and asymptotic local level behavior of weighted KS tests which are either tail, intermediate or central sensitive. Furthermore, we provide new tests with approximately equal local levels and prove that the as...
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作者：Fryzlewicz, Piotr
作者单位：University of London; London School Economics & Political Science
摘要：This article proposes a tail-greedy, bottom-up transform for one-dimensional data, which results in a nonlinear but conditionally orthonormal, multiscale decomposition of the data with respect to an adaptively chosen unbalanced Haar wavelet basis. The tail-greediness of the decomposition algorithm, whereby multiple greedy steps are taken in a single pass through the data, both enables fast computation and makes the algorithm applicable in the problem of consistent estimation of the number and ...
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作者：Minsker, Stanislav
作者单位：University of Southern California
摘要：Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as principal component analysis. However, frequently used empirical covariance estimator, and its modifications, is very sensitive to the presence of outliers in the data. As P. Huber wrote [Ann. Math. Stat. 35 (1964) 73-101], ... This raises a question which could have been asked already by Gauss, but which was, as far as I kno...
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作者：Neumann, Christoph; Kunert, Joachim
作者单位：Dortmund University of Technology
摘要：In crossover designs, each subject receives a series of treatments one after the other. Most papers on optimal crossover designs consider an estimate which is corrected for carryover effects. We look at the estimate for direct effects of treatment, which is not corrected for carryover effects. If there are carryover effects, this estimate will be biased. We try to find a design that minimizes the mean square error, that is, the sum of the squared bias and the variance. It turns out that the de...
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作者：Wang, Lin; Xiao, Qian; Xu, Hongquan
作者单位：University of California System; University of California Los Angeles; University System of Georgia; University of Georgia
摘要：Maximin distance Latin hypercube designs are commonly used for computer experiments, but the construction of such designs is challenging. We construct a series of maximin Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin L-1-distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns.
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作者：Lauritzen, Steffen; Sadeghi, Kayvan
作者单位：University of Copenhagen; University of Cambridge
摘要：Several types of graphs with different conditional independence interpretations-also known as Markov properties-have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges-lines, arrows, arcs and dotted lines-and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considere...
