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作者：Hsing, Tailen; Brown, Thomas; Thelen, Brian
作者单位：University of Michigan System; University of Michigan; Exponent
摘要：Dense spatial data are commonplace nowadays, and they provide the impetus for addressing nonstationarity in a general way. This paper extends the notion of intrinsic random function by allowing the stationary component of the covariance to vary with spatial location. A nonparametric estimation procedure based on gridded data is introduced for the case where the covariance function is regularly varying at any location. An asymptotic theory is developed for the procedure on a fixed domain by let...
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作者：Huang, Shiqiong; Jin, Jiashun; Yao, Zhigang
作者单位：Carnegie Mellon University; National University of Singapore
摘要：Given n samples X-1, X-2,...,X-n from N(0, Sigma), we are interested in estimating the p x p precision matrix Omega = Sigma(-)1; we assume Omega is sparse in that each row has relatively few nonzeros. We propose Partial Correlation Screening (PCS) as a new row -by -row approach. To estimate the ith row of Omega, 1 <= i <= p, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a stage -wise algorithm, where in each stage, the algorithm upd...
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作者：Delaigle, Aurore
作者单位：University of Melbourne; University of Melbourne
摘要：Peter Hall died in Melbourne on January 9, 2016. He was an extremely prolific researcher and contributed to many different areas of statistics. In this paper, I talk about my experience with Peter and I summarise his main contributions to deconvolution, which include measurement error problems and problems in image analysis.
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作者：Samworth, Richard J.
作者单位：University of Cambridge
摘要：In this article, I summarise Peter Hall's contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him. This article complements [Ann. Statist. 44 (2016) 1821-1836; Ann. Statist. 44 (2016) 1837-1853; Ann. Statist. 44 (2016) 1854-1866 and Ann. Statist. 44 (2016) 1867-1887], which focus on other aspects...
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作者：Delaigle, Aurore; Hall, Peter; Zhou, Wen-Xin
作者单位：University of Melbourne; University of Melbourne; Princeton University
摘要：We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general...
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作者：Chen, Song Xi
作者单位：Peking University; Peking University; Iowa State University
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作者：Zhang, Xiaoke; Wang, Jane-Ling
作者单位：University of Delaware; University of California System; University of California Davis
摘要：Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling plan, be it dense,...
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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...
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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
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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-...
