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作者：Yang, Yun; Tokdar, Surya T.
作者单位：University of California System; University of California Berkeley; Duke University
摘要：Minimax L-2 risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on d = O(log n) important predictors among a list of p predictors, with log p = o(n); (2) the true regression surface depends on O(n) predictors but is an additive function where each additive component is sparse but may contain two or more interacting predictors and may have a smoothness level different from other co...
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作者：Levrard, Clement
作者单位：Inria
摘要：Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of O(1/n), where n is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron. J. Stat. 7 (2013) 1716-1746]. This rate is attained for the empirical risk minimizer strategy, if the source distribution satisfies some regularity conditions. However, the dependency of the average distortion on other parameters is not known, and these results are only ...
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作者：Fougeres, Anne-Laure; de Haan, Laurens; Mercadier, Cecile
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang [Statistics of bivariate extremes (1...
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作者：Bandypadhyay, Soutir; Lahiri, Soumendra N.; Nordman, Daniel J.
作者单位：Lehigh University; North Carolina State University; Iowa State University
摘要：This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FUEL) methodology for time series (on a regular grid), the formulation of the spatial I-DEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures. A spat...
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作者：Gao, Chao; Zhou, Harrison H.
作者单位：Yale University
摘要：Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA were established under various interesting settings. On the other side, Bayesian methods are becoming...
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作者：Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
作者单位：Northeast Normal University - China; Northeast Normal University - China; University of Hong Kong
摘要：Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In ...
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作者：Zhang, Ting; Wu, Wei Biao
作者单位：Boston University; University of Chicago
摘要：This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results a...
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作者：Can, Sami Umut; Einmahl, John H. J.; Khmaladze, Estate V.; Laeven, Roger J. A.
作者单位：University of Amsterdam; Tilburg University; Victoria University Wellington
摘要：Let (X-1, Y-1),..., (X-n, Y-n) be an i.i.d sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima V-i=1(n) X-i and V-i=1(n) Y-i is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on ...
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作者：Zheng, Wei
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin [Ann. Statist. 28 (2000) 1728-1742] and Kunert and Mersmann [J. Statist. Plann. Inference 141 (2011) 1623-1632]. Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency unde...
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作者：Vogt, Michael; Dette, Holger
作者单位：University of Konstanz; Ruhr University Bochum
摘要：In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong paramet...
