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作者：Ding, Xiucai; Ma, Rong
作者单位：University of California System; University of California Davis; Stanford University
摘要：We propose a kernel-spectral embedding algorithm for learning lowdimensional nonlinear structures from noisy and high-dimensional observations, where the data sets are assumed to be sampled from a nonlinear manifold model and corrupted by high-dimensional noise. The algorithm employs an adaptive bandwidth selection procedure which does not rely on prior knowledge of the underlying manifold. The obtained low-dimensional embeddings can be further utilized for downstream purposes such as data vis...
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作者：Dumbgen, Lutz; Wellner, Jon A.
作者单位：University of Bern
摘要：We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multiscale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform empirical process U-n(t)/root t (1 - t) and its natural limiting process, the normalized Brownian bridge process U(t)/root t (1 - t). The new tests and confidence bands refine the procedures of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high power ...
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作者：Berg, Stephen; Song, Hyebin
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We exam...
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作者：Reeve, Henry W. J.; Cannings, Timothy I.; Samworth, Richard J.
作者单位：University of Bristol; University of Edinburgh; University of Edinburgh; Heriot Watt University; University of Cambridge
摘要：In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Fo-cusing on a regression setting, we consider the subgroup selection challenge of identifying a region of the feature space on which the regression func-tion exceeds a pre-determined threshold. We formulate the problem as one of constrained optimisation, where we seek a low-c...
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作者：Liu, Zhijun; Hu, Jiang; Bai, Zhidong; Song, Haiyan
作者单位：Northeast Normal University - China
摘要：In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a nontrivial extension of the Bai-Silverstein theorem (BST) (Ann. Probab. 32 (2004) 553-605), a theorem that has strongly influenced the development of high-dimensional statistics, especially in the applications of random matrix theory to statistics. Recently...
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作者：Schell, Alexander; Oberhauser, Harald
作者单位：University of Oxford
摘要：We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with 'non-degenerate' second-order statistics. The lat...
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作者：Ding, Xiucai; Zhou, Zhou
作者单位：University of California System; University of California Davis; University of Toronto
摘要：Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well ap-proximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a struc-tural approximation result is established...
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作者：Armillotta, Mirko; Fokianos, Konstantinos
作者单位：Vrije Universiteit Amsterdam; University of Cyprus
摘要：We study general nonlinear models for time series networks of integer and continuous-valued data. The vector of high-dimensional responses, measured on the nodes of a known network, is regressed nonlinearly on its lagged value and on lagged values of the neighboring nodes by employing a smooth link function. We study stability conditions for such multivariate process and develop quasi-maximum likelihood inference when the network dimension is increasing. In addition, we study linearity score t...
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作者：Baek, Changryong; Duker, Marie-christine; Pipiras, Vladas
作者单位：Sungkyunkwan University (SKKU); Cornell University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：This work develops nonasymptotic theory for estimation of the longrun variance matrix and its inverse, the so-called precision matrix, for highdimensional time series under general assumptions on the dependence structure including long-range dependence. The estimation involves shrinkage techniques, which are thresholding and penalizing versions of the classical multivariate local Whittle estimator. The results ensure consistent estimation in a double asymptotic regime where the number of compo...
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作者：Reiss, Markus; Winkelmann, Lars
作者单位：Humboldt University of Berlin; Free University of Berlin
摘要：We study the rank of the instantaneous or spot covariance matrix ⠂X (t) of a multidimensional process X (t). Given high-frequency observations X(i/n), i = 0, ... , n, we test the null hypothesis rank(⠂X(t)) & LE; r for all t against local alternatives where the average (r + 1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends ...
