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作者：Schoen, Eric D.; Eendebak, Pieter T.; Goos, Peter
作者单位：KU Leuven; Netherlands Organization Applied Science Research; University of Antwerp
摘要：A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row and -1's and +1's elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on o...
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作者：Neykov, Matey; Liu, Han
作者单位：Carnegie Mellon University; Northwestern University
摘要：This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can...
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作者：Zhou, Bo; van den Akker, Ramon; Werker, Bas J. M.
作者单位：Hong Kong University of Science & Technology; Tilburg University; Tilburg University
摘要：We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true ...
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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：In this paper, the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressi...
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作者：Bhattacharya, Anirban; Pati, Debdeep; Yang, Yun
作者单位：Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback-Leibler (KL) neighborhood of the true parameter (or the KL divergence minimizer in the misspeci...
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作者：De Castro, Yohann; Gamboa, Fabrice; Henrion, Didier; Hesst, Roxana; Lasserre, Jean-Bernard
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semialgebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This article shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy in...
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作者：Kontorovich, Aryeh; Pinelis, Iosif
作者单位：Ben-Gurion University of the Negev; Michigan Technological University
摘要：We provide an exact nonasymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-approximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized voting procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form c(infinity)/root nu as v -> infinity, where c(infinity) = 0.16997... is a universal ...
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作者：Chen, Song Xi; Li, Jun; Zhong, Ping-Shou
作者单位：Peking University; Peking University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Michigan State University
摘要：This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate L-2-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal enhancement. It is shown tha...
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作者：Cook, R. Dennis; Forzani, Liliana
作者单位：University of Minnesota System; University of Minnesota Twin Cities; National University of the Littoral
摘要：We study the asymptotic behavior of predictions from partial least squares (PLS) regression as the sample size and number of predictors diverge in various alignments. We show that there is a range of regression scenarios where PLS predictions have the usual root-n convergence rate, even when the sample size is substantially smaller than the number of predictors, and an even wider range where the rate is slower but may still produce practically useful results. We show also that PLS predictions ...
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作者：Zhang, Anru
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In addition, the implementation of some previous methods are NP-hard. In this article, we propose a framework for low-rank tensor completion via a novel tensor measurement scheme that ...
