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作者：McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew; Pillai, Natesh
作者单位：Duke University; Duke University; Duke University; University of North Carolina; University of North Carolina Chapel Hill; Harvard University
摘要：We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimatio...
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作者：Ma, Shujie; Carroll, Raymond J.; Liang, Hua; Xu, Shizhong
作者单位：University of California System; University of California Riverside; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney; George Washington University; University of California System; University of California Riverside
摘要：In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the large p small n setting...
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作者：Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy
作者单位：Princeton University; University of Chicago
摘要：We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major c...
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作者：Fan, Yingying; Kong, Yinfei; Li, Daoji; Zheng, Zemin
作者单位：University of Southern California; University of Southern California; University of Southern California
摘要：This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (ITS) approach based on transforming the original p-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and simultaneously conducting cl...
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作者：Sarkar, Purnamrita; Bickel, Peter J.
作者单位：University of Texas System; University of Texas Austin; University of California System; University of California Berkeley
摘要：Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comp...
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作者：Byrne, Simon; Dawid, A. Philip
作者单位：University of London; University College London; University of Cambridge
摘要：This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis and comparison of mu...
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作者：Maathuis, Marloes H.; Colombo, Diego
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explic...
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作者：Bhattacharyya, Sharmodeep; Bickel, Peter J.
作者单位：University of California System; University of California Berkeley; Oregon State University
摘要：Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or moments (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280-2301]) and smooth functions of these features for the networks. Using these methods,...
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作者：Steinwart, Ingo
作者单位：University of Stuttgart
摘要：The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components. In the case where this algorithm is fed with histogram-based level set estimates, we provide a finite sample analysis, which is then u...
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作者：Jacob, Pierre E.; Thiery, Alexandre H.
作者单位：University of Oxford; National University of Singapore
摘要：We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function f and a sequence of unbiased estimators of lambda is an element of R, there is no algorithm yielding almost surely nonnegative unbiased estimators of f(lambda) is an element of R+. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow exact inference in intractable m...
