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作者：Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze
作者单位：North Carolina State University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penal...
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作者：Fan, Zhou; Johnstone, Iain M.
作者单位：Yale University; Stanford University
摘要：We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedu...
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作者：Chen, Wei-Kuo
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider the problem of detecting a deformation from a symmetric Gaussian random p-tensor (p >= 3) with a rank-one spike sampled from the Rademacher prior. Recently, in Lesieur et al. (Barbier, Krzakala, Macris, Miolane and Zdeborova (2017)), it was proved that there exists a critical threshold beta(p) so that when the signal-to-noise ratio exceeds beta(p), one can distinguish the spiked and unspiked tensors and weakly recover the prior via the minimal mean-square-error method. On the other...
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作者：Doss, Charles R.; Wellner, Jon A.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle
摘要：We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained maximum likelihood estimator where the constraint is that the mode of the density is fixed, say at m. The constrained estimation problem is studied in detail in Doss and Wellner (2018). Here, the results of that paper are used to show that, under...
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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：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：Lian, Heng; Zhao, Kaifeng; Lv, Shaogao
作者单位：City University of Hong Kong; Philips; Philips Research; Nanjing Audit University
摘要：In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to th...
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作者：Zhang, Anru; Brown, Lawrence D.; Cai, T. Tony
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania
摘要：We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses (labels). Otherwise, the formulation is assumption-lean in that no major conditions are imposed on the statistical or functional form of the data. We consider both the ideal semi-supervised setting where infinitel...
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作者：Zheng, Shurong; Cheng, Guanghui; Guo, Jianhua; Zhu, Hongtu
作者单位：Northeast Normal University - China; Northeast Normal University - China; Guangzhou University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one , two and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and sparse alternatives. ...
