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作者：Cuesta-Albertos, Juan A.; Garcia-Portugues, Eduardo; Febrero-Bande, Manuel; Gonzalez-Manteiga, Wenceslao
作者单位：Universidad de Cantabria; Universidade de Santiago de Compostela
摘要：We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that exhibit root-n convergence rates and circumvent the curse of dimensionality. The weak convergence of the empirical process is obtained conditionally on a random direction, whilst th...
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作者：Chen, Xiaohui; Kato, Kengo
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Cornell University
摘要：This paper studies inference for the mean vector of a high-dimensional U -statistic. In the era of big data, the dimension d of the U-statistic and the sample size n of the observations tend to be both large, and the computation of the U -statistic is prohibitively demanding. Data-dependent inferential procedures such as the empirical bootstrap for U -statistics is even more computationally expensive. To overcome such a computational bottleneck, incomplete U-statistics obtained by sampling few...
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作者：Dette, Holger; Wu, Weichi
作者单位：Ruhr University Bochum; Ruhr University Bochum; Tsinghua University
摘要：This paper considers the problem of testing if a sequence of means (mu(t))(t=1, ...,n) of a nonstationary time series (X-t)(t=1, )(...,n) is stable in the sense that the difference of the means mu(1) and mu(t )between the initial time t = 1 and any other time is smaller than a given threshold, that is vertical bar mu(1) - mu(t)vertical bar <= c for all t = 1, ..., n. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic...
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作者：Veitch, Victor; Roy, Daniel M.
作者单位：Columbia University; University of Toronto
摘要：Sparse exchangeable graphs on R+, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on N, and the associated graphon framework for dense graphs. We develop the graphex framework as a tool for statistical network analysis by identifying the sampling scheme that is naturally associated with the models of the framework, formalizing two natural notions of consistent estimation of the parameter (the graphex) underlying these models, and identifying general consi...
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作者：Richter, Stefan; Dahlhaus, Rainer
作者单位：Ruprecht Karls University Heidelberg
摘要：We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.
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作者：Descary, Marie-Helene; Panaretos, Victor M.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretabilit...
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作者：Chen, Yuxin; Fan, Jianqing; Ma, Cong; Wang, Kaizheng
作者单位：Princeton University; Fudan University; Princeton University
摘要：This paper is concerned with the problem of top-K ranking from pairwise comparisons. Given a collection of n items and a few pairwise comparisons across them, one wishes to identify the set of K items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model-the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Re...
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作者：Raskutti, Garvesh; Yuan, Ming; Chen, Han
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：In this paper, we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable regularizers assuming that the underlying tensor lies in an unknown low-dimensional subspace. Within our framework, we derive general risk bounds of the resulting estimate under fairly general dependence structure among covariates. Our framework leads to upper bou...
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作者：Bing, Xin; Wegkamp, Marten H.
作者单位：Cornell University; Cornell University
摘要：We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the one proposed in Bunea, She and Wegkamp (Ann. Statist. 39 (2011) 1282-1309) in that it does not require estimation of the unknown variance of the noise, nor does it depend on a delicate choice of a tuning parameter. We develop an iterative, fully data-driven ...
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作者：Feng, Long; Zhang, Cun-Hui
作者单位：City University of Hong Kong; Rutgers University System; Rutgers University New Brunswick
摘要：The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and estimation, the bias of the Lasso can be also reduced by taking a smaller penalty level than what selection consistency requires, but such smaller penalty level depends on the sparsity of the true coefficient vector. The sorted l(1) penalized estimation (Slo...
