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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...
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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...
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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-...
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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...
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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...
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作者：Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We revisit, in an original and challenging perspective, the problem of testing the null hypothesis that the mode of a directional signal is equal to a given value. Motivated by a real data example where the signal is weak, we consider this problem under asymptotic scenarios for which the signal strength goes to zero at an arbitrary rate eta(n). Both under the null and the alternative, we focus on rotationally symmetric distributions. We show that, while they are asymptotically equivalent under...
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作者：Zhu, Ying
作者单位：Michigan State University
摘要：We consider a two-step projection based Lasso procedure for estimating a partially linear regression model where the number of coefficients in the linear component can exceed the sample size and these coefficients belong to the l(q) -balls for q is an element of [0, 1]. Our theoretical results regarding the properties of the estimators are nonasymptotic. In particular, we establish a new nonasymptotic oracle result: Although the error of the nonparametric projection per se (with respect to the...
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作者：Jiang, Tiefeng; Leder, Kevin; Xu, Gongjun
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; University of Michigan System; University of Michigan
摘要：In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulat...
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作者：Shi, Peibei; Qu, Annie
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Weak signal identification and inference are very important in the area of penalized model selection, yet they are underdeveloped and not well studied. Existing inference procedures for penalized estimators are mainly focused on strong signals. In this paper, we propose an identification procedure for weak signals in finite samples, and provide a transition phase in-between noise and strong signal strengths. We also introduce a new two-step inferential method to construct better confidence int...
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作者：Yang, Yun; Pilanci, Mert; Wainwright, Martin J.
作者单位：State University System of Florida; Florida State University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n(3)) and O(n(2)), respectively, and so is prohibitive in many cases. We propose approximations of KRR based on m-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension m can be chosen while still preserving minimax optimality of the ...
