-
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...
-
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 ...
-
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...
-
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...
-
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 ...
-
作者：Cutting, Christine; Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in nonnull issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The first one is for fixed modal location. and allows to derive locally asymptotically most powerful tests under specified.. The second one, that addresses the Fisher-von Mises-Langevin (FvML) case, relates to the unspecified-theta problem and shows that the high-d...
-
作者：Li, Bing; Song, Jun
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where both the predictor and the response may be random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads to construction of two functional spaces: the first representing the functional data, assumed to be a Hilbert space, and the second cha...
-
作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodnessof- fit tests. In this paper, we give a new goodness-of-fit test for volatilitylike processes, which is easily applied to a variety of semimartingale models. In each case, we reduce the problem to the detection of a semimartingale observed under noise. In this setting, we then describe a wavelet-thresholding test, which obtains adaptive and near-...
-
作者：Wang, Weichen; Fan, Jianqing
作者单位：Princeton University
摘要：We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size and dimensionality play in principal component analysis. Our results are a natural extension of those in [Statist. Sinica 1...
-
作者：Zhu, Xuening; Pan, Rui; Li, Guodong; Liu, Yuewen; Wang, Hansheng
作者单位：Peking University; Central University of Finance & Economics; University of Hong Kong; Xi'an Jiaotong University
摘要：We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node's response at a given time point as a linear combination of (a) its previou...
