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作者：Ji, Pengsheng; Jin, Jiashun
作者单位：Cornell University; Carnegie Mellon University
摘要：Consider a linear model Y = X beta + z, z similar to N(0, I-n). Here, X = X-n,X-p, where both p and n are large, but p > n. We model the rows of X as lid. samples from N(0, 1/n Omega), where Omega is a p x p correlation matrix, which is unknown to us but is presumably sparse. The vector beta is also unknown but has relatively few nonzero coordinates, and we are interested in identifying these nonzeros. We propose the Univariate Penalization Screeing (UPS) for variable selection. This is a scre...
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作者：Xu, Ganggang; Huang, Jianhua Z.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asympto...
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作者：Zhao, Yunpeng; Levina, Elizaveta; Zhu, Ji
作者单位：George Mason University; University of Michigan System; University of Michigan
摘要：Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of community detection under the block model have been recently developed. However, the block model is limited by its assumption that all nodes within a community are stochastically equivalent, and provides a poor fit to networks with hubs or highly varying node d...
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作者：Bercu, Bernard; Fraysse, Philippe
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make u...
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作者：Delaigle, Aurore; Hall, Peter
作者单位：University of Melbourne; University of California System; University of California Davis
摘要：The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attracti...
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作者：Romano, Joseph P.; Shaikh, Azeem M.
作者单位：Stanford University; Stanford University; University of Chicago
摘要：This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions P. These results are then applied (i) to construct confidence regions that behave well uniformly over P in the sense that the coverage probability tends to at least the nominal level uniformly over P and (ii) to construct tests that behave well uniformly over P in the sense that...
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作者：Dou, Winston Wei; Pollard, David; Zhou, Harrison H.
作者单位：Yale University
摘要：This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equiv...
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作者：Lee, Young K.; Mammen, Enno; Park, Byeong U.
作者单位：Kangwon National University; University of Mannheim; Seoul National University (SNU)
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作者：Li, Gaorong; Peng, Heng; Zhang, Jun; Zhu, Lixing
作者单位：Beijing University of Technology; Hong Kong Baptist University; Shenzhen University
摘要：Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or large p, small n paradigms when p can be as large as an exponential of the sample size n. In this paper we propose a robust rank correlation screening (RRCS) method to deal with ultra-high dimensional data. The new procedure is based on the Kendall tau correlation coefficient between response and predictor ...
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作者：Guntuboyina, Adityanand
作者单位：University of Pennsylvania
摘要：We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.
