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作者：Schmidt-Hieber, Johannes; Schneider, Laura Fee; Staudt, Thomas; Krajina, Andrea; Aspelmeier, Timo; Munk, Axel
作者单位：University of Twente; University of Gottingen; Max Planck Society; University of Gottingen; UNIVERSITY GOTTINGEN HOSPITAL
摘要：Estimation of the population size n from k i.i.d. binomial observations with unknown success probability p is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously difficult task when p becomes small, and the Bayesian approach becomes particularly useful. For a large class of priors, we establish posterior contraction and a Bernstein-von Mises type theorem in a setting where p -> 0 and n -> infinity as k -> infinity. Furtherm...
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作者：Bickel, Peter; Fiocco, Marta; de Gunst, Mathisca; Goetze, Friedrich
作者单位：University of California System; University of California Berkeley; Leiden University; Leiden University - Excl LUMC; Vrije Universiteit Amsterdam; University of Bielefeld
摘要：Willem van Zwet made deep and influential contributions to probability and statistics, which we review in this paper. Bickel and Gotze collaborated with him on his major contributions to higher order asymptotics of nonlinear statistics and on resampling and the bootstrap. We relate this work to his remarkable development of the properties of the Hoeffding expansion for symmetric statistics as well as Fourier analytic tools. Fiocco and De Gunst were his students. We describe how in their theses...
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作者：Lee, Donald K. K.; Chen, Ningyuan; Ishwaran, Hemant
作者单位：Emory University; Emory University; University of Toronto; University of Miami
摘要：Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric loglikelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent if the model is corr...
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作者：Chetverikov, Denis; Liao, Zhipeng; Chernozhukov, Victor
作者单位：University of California System; University of California Los Angeles; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In this paper, we derive nonasymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using K-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, L-2, and L-1 norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation error of the cross-validate...
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作者：Fang, Billy; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We consider the problem of nonparametric regression when the covariate is d dimensional, where d >= 1. In this paper, we introduce and study two non-parametric least squares estimators (LSEs) in this setting-the entirely monotonic LSE and the constrained Hardy-Krause variation LSE. We show that these two LSEs are natural generalizations of univariate isotonic regression and univariate total variation denoising, respectively, to multiple dimensions. We discuss the characterization and computati...
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作者：Lei, Jing
作者单位：Carnegie Mellon University
摘要：Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work, we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in t...
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作者：Pollak, Moshe
作者单位：Hebrew University of Jerusalem
摘要：Consider a process that produces a series of independent identically distributed vectors. A change in an underlying state may become manifest in a modification of one or more of the marginal distributions. Often, the dependence structure between coordinates is unknown, impeding surveillance based on the joint distribution. A popular approach is to construct control charts for each coordinate separately and raise an alarm the first time any (or some) of the control charts signals. The difficult...
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作者：Xia, Dong; Yuan, Ming; Zhang, Cun-Hui
作者单位：Hong Kong University of Science & Technology; Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundamental computational challenges often associated with problems involving higher order tensors, yet very little is known about their statistical performance. To fill in this void, in...
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作者：Horvath, Lajos; Kokoszka, Piotr; Wang, Shixuan
作者单位：Utah System of Higher Education; University of Utah; Colorado State University System; Colorado State University Fort Collins; University of Reading
摘要：We propose a method for the detection of a change point in a sequence {F-i} of distributions, which are available through a large number of observations at each i >= 1. Under the null hypothesis, the distributions F-i are equal. Under the alternative hypothesis, there is a change point i * > 1, such that F-i = G for i >= i* and some unknown distribution G, which is not equal to F-1. The change point, if it exists, is unknown, and the distributions before and after the potential change point ar...
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作者：Najafi, Amir; Ilchi, Saeed; Saberi, Amir Hossein; Motahari, Seyed Abolfazl; Khalaj, Babak H.; Rabiee, Hamid R.
作者单位：Sharif University of Technology; Sharif University of Technology; Sharif University of Technology
摘要：We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of spectral unmixing. We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of is an element of is O(K-2/epsilon log K/epsilon), wh...
