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作者：Fan, Jianqing; Liu, Han; Sun, Qiang; Zhang, Tong
作者单位：Fudan University; Princeton University; Princeton University; University of Toronto
摘要：We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high-dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second...
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作者：Paindaveine, Davy; Van Bever, Germain
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept is similar to those from Chen, Gao and Ren [Robust covariance and scatter matrix estimation under Huber's contamination model (2018)] and Zhang [J. Multivariate Anal. 82 (2002) 134-165]. Rather than focusing, as in these earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so unde...
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作者：Bellec, Pierre C.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax rate of aggregation is of order log(M), where M is the number of estimators to aggregate. It is proved that for affine estimators, the minimax rate of aggregation is unchanged: it is possible to handle the linear dependence between the affine estimators and th...
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作者：Leung, Dennis; Drton, Mathias
作者单位：Chinese University of Hong Kong; University of Washington; University of Washington Seattle
摘要：We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank correlations. In the asymptotic regime where both m and n tend to infinity, a martingale central limit theorem is applied to show that the null distributions of these statistics converge to Gaussian limits, which are valid with no specific distributional or m...
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作者：Perry, Amelia; Wein, Alexander S.; Bandeira, Afonso S.; Moitra, Ankur
作者单位：Massachusetts Institute of Technology (MIT); New York University; New York University; Massachusetts Institute of Technology (MIT)
摘要：A central problem of random matrix theory is to understand the eigen-values of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or spike) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical thr...
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作者：Chen, Yudong; Li, Xiaodong; Xu, Jiaming
作者单位：Cornell University; University of California System; University of California Davis; Purdue University System; Purdue University
摘要：The stochastic block model (SBM), a popular framework for studying community detection in networks, is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. To find the communities under DCSBM, this paper proposes a convexified modularity maximization approach, which is based on a convex...
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作者：Behr, Merle; Holmes, Chris; Munk, Axel
作者单位：University of Gottingen; University of Oxford; Max Planck Society
摘要：We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an epsilon-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and ...
