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作者：Li, Degui; Ke, Yuan; Zhang, Wenyang
作者单位：University of York - UK
摘要：In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO penalty (or the local l...
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作者：Fan, Yingying; James, Gareth M.; Radchenk, Peter
作者单位：University of Southern California
摘要：We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, X(t), and a scalar response, Y, in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, FAR extends beyond the standard linear regression se...
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作者：Bickel, Peter J.; Chen, Aiyou; Zhao, Yunpeng; Levina, Elizaveta; Zhu, Ji
作者单位：University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated; George Mason University; University of Michigan System; University of Michigan
摘要：This note corrects an error in two related proofs of consistency of community detection: under stochastic block models by Bickel and Chen [Proc. Natl. Acad. ScL USA 106 (2009) 21068-21073] and under degree-corrected stochastic block model by Zhao, Levina and Zhu [Ann. Statist. 40 (2012) 2266-2292].
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作者：Groeneboom, Piet; Jongbloed, Geurt
作者单位：Delft University of Technology
摘要：We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699-1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method with a new proof of the results of Banerjee-Wellner [Ann. Statist. 29 (2001) 1699-1731] and also by constructing confidence ...
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作者：Chichignoud, Michael; Loustau, Sebastien
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Universite d'Angers
摘要：In this paper, we deal with the data-driven selection of multidimensional and possibly anisotropic bandwidths in the general framework of kernel empirical risk minimization. We propose a universal selection rule, which leads to optimal adaptive results in a large variety of statistical models such as nonparametric robust regression and statistical learning with errors in variables. These results are stated in the context of smooth loss functions, where the gradient of the risk appears as a goo...
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作者：Desgagne, Alain
作者单位：University of Quebec; University of Quebec Montreal
摘要：Estimating the location and scale parameters is common in statistics, using, for instance, the well-known sample mean and standard deviation. However, inference can be contaminated by the presence of outliers if modeling is done with light-tailed distributions such as the normal distribution. In this paper, we study robustness to outliers in location-scale parameter models using both the Bayesian and frequentist approaches. We find sufficient conditions (e.g., on tail behavior of the model) to...
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作者：Meinshausen, Nicolai; Buehlmann, Peter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information t...
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作者：Szabo, Botond; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Eindhoven University of Technology; Leiden University; Leiden University - Excl LUMC; University of Amsterdam
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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：Lei, Jing; Vu, Vincent Q.
作者单位：Carnegie Mellon University; University System of Ohio; Ohio State University
摘要：The presence of a sparse truth has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and unique truth? We ans...
