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作者：Berrett, Thomas B.; Kontoyiannis, Ioannis; Samworth, Richard J.
作者单位：University of Warwick; University of Cambridge
摘要：We study the problem of independence testing given independent and identically distributed pairs taking values in a sigma-finite, separable measure space. Defining a natural measure of dependence D(f) as the squared L-2 distance between a joint density f and the product of its marginals, we first show that there is no valid test of independence that is uniformly consistent against alternatives of the form {f : D(f) >= rho(2) }. We therefore restrict attention to alternatives that impose additi...
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作者：Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; Columbia University
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作者：Chen, Yuxin; Fan, Jianqing; Ma, Cong; Yan, Yuling
作者单位：Princeton University; Princeton University; University of Chicago
摘要：This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis in the presence of random noise) remains highly sub...
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作者：Jeon, Jeong Min; Park, Byeong U.; Van Keilegom, Ingrid
作者单位：KU Leuven; Seoul National University (SNU)
摘要：Additive regression is studied in a very general setting where both the response and predictors are allowed to be non-Euclidean. The response takes values in a general separable Hilbert space, whereas the predictors take values in general semimetric spaces, which covers a very wide range of nonstandard response variables and predictors. A general framework of estimating additive models is presented for semimetric space-valued predictors. In particular, full details of implementation and the co...
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作者：Chen, Song Xi; Peng, Liuhua
作者单位：Peking University; Peking University; University of Melbourne
摘要：This paper considers distributed statistical inference for general symmetric statistics in the context of massive data with efficient computation. Estimation efficiency and asymptotic distributions of the distributed statistics are provided, which reveal different results between the nondegenerate and degenerate cases, and show the number of the data subsets plays an important role. Two distributed bootstrap methods are proposed and analyzed to approximation the underlying distribution of the ...
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作者：Bongers, Stephan; Forre, Patrick; Peters, Jonas; Mooij, Joris M.
作者单位：University of Amsterdam; University of Copenhagen; University of Amsterdam
摘要：Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the conve...
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作者：Drton, Mathias; Kuriki, Satoshi; Hoff, Peter
作者单位：Technical University of Munich; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Duke University
摘要：In matrix-valued datasets the sampled matrices often exhibit correlations among both their rows and their columns. A useful and parsimonious model of such dependence is the matrix normal model, in which the covariances among the elements of a random matrix are parameterized in terms of the Kronecker product of two covariance matrices, one representing row covariances and one representing column covariance. An appealing feature of such a matrix normal model is that the Kronecker covariance stru...
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作者：van de Geer, Sara; Klaassen, Chris A. J.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Amsterdam
摘要：Willem van Zwet was supervisor of sixteen PhD students. All of them pursued academic careers and most of them became full professor. Below are some stories of PhD students Wim Albers, Cees Diks, Ronald Does, Marta Fiocco, Sara van de Geer, Mathisca de Gunst, Chris Klaassen, Hein Putter, Aad van der Vaart, Marten Wegkamp and Martien van Zuijlen with in addition a contribution by Nelly Litvak who was guided by Willem after her PhD.
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作者：Lin, Zhantao; Flournoy, Nancy; Rosenberger, William F.
作者单位：George Mason University; University of Missouri System; University of Missouri Columbia
摘要：Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients' biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture of normal distribut...
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作者：Loeffler, Matthias; Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Pennsylvania; Yale University
摘要：Spectral clustering is one of the most popular algorithms to group high-dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian mixture model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are...
