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作者：Hayashi, Masahito; Watanabe, Shun
作者单位：Nagoya University; National University of Singapore; Tokyo University of Agriculture & Technology
摘要：We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.
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作者：Lam, Clifford
作者单位：University of London; London School Economics & Political Science
摘要：We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size...
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作者：Cai, T. Tony; Liu, Weidong; Zhou, Harrison H.
作者单位：University of Pennsylvania; Shanghai Jiao Tong University; Shanghai Jiao Tong University; Yale University
摘要：Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained l(1) minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The estimator, called ACLIME, is e...
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作者：Cai, Tony; Kim, Donggyu; Wang, Yazhen; Yuan, Ming; Zhou, Harrison H.
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison; Yale University
摘要：Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions, for a proof of its...
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作者：Sadeghi, Kayvan
作者单位：University of Cambridge
摘要：In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs aft...
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作者：Cai, T. Tony; Eldar, Yonina C.; Li, Xiaodong
作者单位：University of Pennsylvania; Technion Israel Institute of Technology; University of California System; University of California Davis
摘要：In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram ov...
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作者：Fromont, Magalie; Lerasle, Matthieu; Reynaud-Bourett, Patricia
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite Rennes 2
摘要：Starting from a parallel between some minimax adaptive tests of a single null hypothesis, based on aggregation approaches, and some tests of multiple hypotheses, we propose a new second kind error-related evaluation criterion, as the core of an emergent minimax theory for multiple tests. Aggregation based tests, proposed for instance by Baraud [Bernoulli 8 (2002) 577-606], Baraud, Huet and Laurent [Ann. Statist. 31 (2003) 225-251] or Fromont and Laurent [Ann. Statist. 34 (2006) 680-720], are j...
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作者：Yu, Zhou; Dong, Yuexiao; Shao, Jun
作者单位：East China Normal University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Wisconsin System; University of Wisconsin Madison
摘要：Model-free variable selection has been implemented under the sufficient dimension reduction framework since the seminal paper of Cook [Ann. Statist. 32 (2004) 1062-1092]. In this paper, we extend the marginal coordinate test for sliced inverse regression (SIR) in Cook (2004) and propose a novel marginal SIR utility for the purpose of ultrahigh dimensional feature selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to get two versions of...
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作者：Chen, Song Xi
作者单位：Peking University; Peking University; Iowa State University
