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作者：Zhang, Bo; Pan, Guangming; Gao, Jiti
作者单位：Nanyang Technological University; Monash University
摘要：Let {Z(ij)} be independent and identically distributed (i.i.d.) random variables with EZ(ij) = 0, E vertical bar Z(ij)vertical bar(2) = 1 and E vertical bar Z(ij)vertical bar(4) < infinity. Define linear processes Y-tj = Sigma(infinity)(k=0) b(k) Z(t -k,j) with Sigma(infinity)(i=0) vertical bar b(i)vertical bar < infinity. Consider a p-dimensional time series model of the form x(t) = Pi x(t-1) + Sigma(1/2)y(t), 1 <= t <= T with y(t) = (Y-t(1), ..., Y-tp)' and Sigma(1/2) be the square root of a...
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作者：Sienkiewicz, Ela; Wang, Haonan
作者单位：Colorado State University System; Colorado State University Fort Collins
摘要：In this paper, we consider a set of unlabeled tree objects with topological and geometric properties. For each data object, two curve representations are developed to characterize its topological and geometric aspects. We further define the notions of topological and geometric medians as well as quantiles based on both representations. In addition, we take a novel approach to define the Pareto medians and quantiles through a multi-objective optimization problem. In particular, we study two dif...
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作者：Xia, Ningning; Zheng, Xinghua
作者单位：Shanghai University of Finance & Economics; Hong Kong University of Science & Technology
摘要：In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noisetype sample covariance matrices. As an application, we consi...
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作者：Dai, Xiongtao; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered, for example, as movement trajectories on the surface of the earth are an important special case. We consider an intrinsic principal component analysis for smooth Riemannian manifold-valued functional data and study its asymptotic properties. Riemannian functional principal component analysis (RFPCA) is carried out by first mapping the manifold-valued data through Rie...
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作者：Escobar-Bach, Mikael; Goegebeur, Yuri; Guillou, Armelle
作者单位：University of Southern Denmark; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We consider the robust estimation of the Pickands dependence function in the random covariate framework. Our estimator is based on local estimation with the minimum density power divergence criterion. We provide the main asymptotic properties, in particular the convergence of the stochastic process, correctly normalized, towards a tight centered Gaussian process. The finite sample performance of our estimator is evaluated with a simulation study involving both uncontaminated and contaminated s...
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作者：Tang, Minh; Priebe, Carey E.
作者单位：Johns Hopkins University
摘要：We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized Laplacian converge to multivariate normals and, furthermore, the mean and the covariance matrix of each row are functions of the associated vertex's block membership. Together with p...
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作者：Zhou, Wen-Xin; Bose, Koushiki; Fan, Jianqing; Liu, Han
作者单位：University of California System; University of California San Diego; Princeton University; Fudan University
摘要：Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [Ann. Statist. 1 (1973) 799-821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. In this paper, ...
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作者：Donoho, David; Gavish, Matan; Johnstone, Iain
作者单位：Stanford University; Hebrew University of Jerusalem
摘要：We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework based on the spiked covariance model and use of orthogonally invariant estimators, we show that optimal estimation of the population covariance matrix boils down to design of an optimal shrinker eta that acts elementwise on the sample eigenvalues. Indeed, to each loss function there corresponds a unique admissible eigenvalue shrinker et...
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作者：Doss, Hani; Park, Yeonhee
作者单位：State University System of Florida; University of Florida; University of Texas System; UTMD Anderson Cancer Center
摘要：Consider a Bayesian situation in which we observe Y similar to p(theta), where theta is an element of Theta and we have a family {vh, h is an element of H} of potential prior distributions on Theta. Let g be a real-valued function of theta, and let I-g(h) be the posterior expectation of g(theta) when the prior is v(h) . We are interested in two problems: (i) selecting a particular value of h, and (ii) estimating the family of posterior expectations {I-g(h), h is an element of H}. Let m(y)(h) b...
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作者：Mukherjee, Rajarshi; Mukherjee, Sumit; Sen, Subhabrata
作者单位：University of California System; University of California Berkeley; Columbia University; Microsoft; Microsoft
摘要：In this paper, we study sharp thresholds for detecting sparse signals in beta-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity and signal strength. In regimes of moderately dense signals, irrespective of graph sparsity, the detection thresholds mirror corresponding results in independent Gaussian sequence problems. For sparser signals, extreme graph sparsity implies that all tests are asymptotically powerless, ir...
