-
作者：Cheng, Ming-Yen; Fan, Jianqing
作者单位：National Taiwan University; Princeton University
摘要：Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape constraints, estimatio...
-
作者：Li, Runze
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
-
作者：Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：Yale University
摘要：Recently, network analysis has gained more and more attention in statistics, as well as in computer science, probability and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives minimax rates of the mis-...
-
作者：El Karoui, Noureddine; Wu, Hau-Tieng
作者单位：University of California System; University of California Berkeley; University of Toronto
摘要：Recently, several data analytic techniques based on graph connection Laplacian (GCL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is observed without noise. We study the impact of additive noise on these methods and show that they are remarkably robust. As a by-product of our analysis, we propose modifications of the standard algorithms that increase their robustness to noise. We illustrate our...
-
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...
-
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...
-
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].
-
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 ...
-
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...
-
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...
