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作者：Miller, Jeffrey W.; Harrison, Matthew T.
作者单位：Brown University
摘要：The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence...
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作者：Anandkumar, Animashree; Valluvan, Ragupathyraj
作者单位：University of California System; University of California Irvine
摘要：The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of correlation decay. For the special case of the Ising model, the number of samples n required for structural consistency of our method scales as n = Omega(theta(-delta eta(eta+1)-2)(m...
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function should be used for estimation of the univariate component. It is known that the scale function does not affect the rate of the MISE convergence, and as a result sharp constants are explored. The paper begins with developing a sharp-minimax theory for a pivotal m...
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作者：Lepski, Oleg
作者单位：Aix-Marseille Universite
摘要：This paper deals with the density estimation on R-d under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multivariate density model. Usefulness of the...
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作者：Chen, Xiaohui; Xu, Mengyu; Wu, Wei Biao
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago
摘要：We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate ...
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作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley
摘要：We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an...
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作者：Xia, Ningning; Qin, Yingli; Bai, Zhidong
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; University of Waterloo
摘要：The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Marcenko-Pastur distribution function is of order O(N-1/2). Given that data dimension n to sample size N ratio is bounded between 0 and 1, this convergence rate is established under finite 10th moment condition of the u...
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作者：Ho, Lam Si Tung; Ane, Cecile
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When observations are modeled using an Ornstein-Uhlenbeck (OU) process along the tree, the autocorrelation between two tips decreases exponentially with their tree distance. These models are most often applied in evolutionary biology, when tips represent biological specie...
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作者：Bickel, Peter; Choi, David; Chang, Xiangyu; Zhang, Hai
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University; Xi'an Jiaotong University; Northwest University Xi'an
摘要：Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.
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作者：Yamagata, Koichi; Fujiwara, Akio; Gill, Richard D.
作者单位：University of Osaka; Leiden University - Excl LUMC; Leiden University
摘要：We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.
