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作者：Hang, Hanyuan; Steinwart, Ingo
作者单位：University of Stuttgart
摘要：We establish a Bernstein-type inequality for a class of stochastic processes that includes the classical geometrically phi-mixing processes, Rio's generalization of these processes and many time-discrete dynamical systems. Modulo a logarithmic factor and some constants, our Bernstein-type inequality coincides with the classical Bernstein inequality for i.i.d. data. We further use this new Bernstein-type inequality to derive an oracle inequality for generic regularized empirical risk minimizati...
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作者：Koltchinskii, Vladimir; Lounici, Karim
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let X, X-1,...,X-n be i.i.d. Gaussian random variables in a separable Hilbert space H with zero mean and covariance operator Sigma = E(X circle times X), and let (Sigma) over cap := n(-1) Sigma(n)(j=1) (X-i circle times X-j) be the sample (empirical) covariance operator based on (XI,..,Xn). Denote by P-r the spectral projector of Sigma corresponding to its rth eigenvalue mu(r) and by (P-r) over cap the empirical counterpart of P-r. The main goal of the paper is to obtain tight bounds on sup(x ...
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作者：Chan, Hock Peng
作者单位：National University of Singapore
摘要：Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the optimal) detection delay depends on the fraction of data streams undergoing distribution changes as the num...
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作者：Aston, John A. D.; Pigoli, Davide; Tavakoli, Shahin
作者单位：University of Cambridge
摘要：The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons, or due to a small sample size. However, inferential tools to verify this assumption are somewhat lacking in high-dimensional or functional data analysis settings, where this assumption is most relevant. We propose here to tes...
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作者：Ando, Tomohiro; Li, Ker-Chau
作者单位：University of Melbourne; University of California System; University of California Los Angeles; Academia Sinica - Taiwan
摘要：Model averaging has long been proposed as a powerful alternative to model selection in regression analysis. However, how well it performs in high-dimensional regression is still poorly understood. Recently, Ando and Li [J. Amer. Statist. Assoc. 109 (2014) 254-265] introduced a new method of model averaging that allows the number of predictors to increase as the sample size increases. One notable feature of Ando and Li's method is the relaxation on the total model weights so that weak signals c...
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作者：Li, Meng; Ghosal, Subhashis
作者单位：Duke University; North Carolina State University
摘要：Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a d-dimensional image (d = 2, 3,...), the boundary can often be described by a closed smooth (d - 1)-dimensional manifold. In this paper, we propose a nonparametric Bayesian approach based on priors indexed by Sd-1, the unit sphere in R-d. We derive optimal posterior contraction rates for Gaussian processes or finite random series priors using basis functions such...
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作者：Zhang, Danna; Wu, Wei Biao
作者单位：University of California System; University of California San Diego; University of Chicago
摘要：We consider the problem of approximating sums of high dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size n, the dimension p, the moment condition and the dependence of the underlying processes. We also consider an estimator for long-run covariance matrices and study its convergence properties. Our results allow constructing simultaneous confidence intervals for mean ...
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作者：Cai, T. Tony; Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Pennsylvania
摘要：We study in this paper computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple nonoverlapping) signal submatrix (of magnitude. and size k(m) x k(n)) embedded in a large noise matrix (of size mxn), the goal is to optimal identify the support of the signal submatrix computationally and statistically. Two transition thresholds for the signal-to-noise ratio lambda/ sigma are established in terms of m, n, k(m) and k(n). The first threshold, SNR...
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作者：Dette, Holger; Konstantinou, Maria; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of observations and considers the asymptotic properties of estimators and designs as the sample size converges to infinity, our approach is based on a continuous time model. We use results from stochastic analysis to identify the best linear unbiased estimator (BL...
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作者：Zheng, Wei; Ai, Mingyao; Li, Kang
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis; Peking University
摘要：Many applications of block designs exhibit neighbor and edge effects. A popular remedy is to use the circular design coupled with the interference model. The search for optimal or efficient designs has been intensively studied in recent years. The circular neighbor balanced designs at distances 1 and 2 (CNBD2), including orthogonal array of type I (OAI) of strength 2, are the two major designs proposed in literature for the purpose of estimating the direct treatment effects. They are shown to ...
