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作者：Carroll, Raymond J.; Delaigle, Aurore; Hall, Peter
作者单位：Texas A&M University System; Texas A&M University College Station; University of Melbourne
摘要：The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show that this approach is ...
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作者：Liu, Weidong
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University
摘要：This paper studies the estimation of a high-dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. In this paper we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional dependence, we pro...
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作者：Naghshvar, Mohammad; Javidi, Tara
作者单位：Qualcomm; University of California System; University of California San Diego
摘要：Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most informative sensing action among the available ones. In this paper, using results in dynamic programming, lower bounds for the optimal...
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作者：Wang, Yazhen
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. R...
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作者：Li, Jia; Todorov, Viktor; Tauchen, George
作者单位：Duke University; Northwestern University
摘要：We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Ito semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estim...
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作者：Birnbaum, Aharon; Johnstone, Iain M.; Nadler, Boaz; Paul, Debashis
作者单位：Hebrew University of Jerusalem; Stanford University; Weizmann Institute of Science; University of California System; University of California Davis
摘要：We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l(2) loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a n...
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作者：Leeb, Hannes
作者单位：University of Vienna
摘要：We study the conditional distribution of low-dimensional projections from high-dimensional data, where the conditioning is on other low-dimensional projections. To fix ideas, consider a random d-vector Z that has a Lebesgue density and that is standardized so that EZ = 0 and EZZ' = I-d. Moreover, consider two projections defined by unit-vectors alpha and beta, namely a response y = alpha'Z and an explanatory variable x = beta'Z. It has long been known that the conditional mean of y given x is ...
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作者：Xuanlong Nguyen
作者单位：University of Michigan System; University of Michigan
摘要：This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of mixing measures and f-divergence functionals such as Hellinger and Kullback-Leibler distances on the space of mixture distributions is investigated in detail using various identifiability conditions. Convergence in Wasserstein metrics for discrete measures im...
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作者：Cai, T. Tony; Ma, Zongming; Wu, Yihong
作者单位：University of Pennsylvania; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation p...
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作者：Amini, Arash A.; Chen, Aiyou; Bickel, Peter J.; Levina, Elizaveta
作者单位：University of Michigan System; University of Michigan; Alphabet Inc.; Google Incorporated; University of California System; University of California Berkeley
摘要：Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the e...
