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作者：Daouia, Abdelaati; Stupfler, Gilles; Usseglio-carleve, Antoine
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite d'Angers; Avignon Universite
摘要：Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. We develop a fully operational inferential theory for extreme conditional quantiles and expectiles in the challenging framework of alpha-mixing, conditional heavy-tailed data whose tail index may vary with covariate values. This requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling difficulties inherent t...
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作者：Dau, Hai-dang; Chopin, Nicolas
作者单位：Institut Polytechnique de Paris; ENSAE Paris
摘要：In the context of state-space models, skeleton-based smoothing algo-rithms rely on a backward sampling step, which by default, has a O(N-2) complexity (where N is the number of particles). Existing improvements in the literature are unsatisfactory: a popular rejection sampling-based approach, as we shall show, might lead to badly behaved execution time; another rejec-tion sampler with stopping lacks complexity analysis; yet another MCMC-inspired algorithm comes with no stability guarantee. We ...
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作者：Chaudhuri, Anamitra; Chatterjee, Sabyasachi
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting crossvalidated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the generality of the f...
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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...
