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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：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：Barber, Rina Foygel; Candes, Emmanuel J.
作者单位：University of Chicago; Stanford University
摘要：In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR) the expected fraction of false discoveries among all discoveries is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff ...
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作者：Castillo, Ismael; Schmidt-Hieber, Johannes; Van der Vaart, Aad
作者单位：Sorbonne Universite; Universite Paris Cite; Leiden University - Excl LUMC; Leiden University
摘要：We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significan...
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作者：Sagnol, Guillaume; Harman, Radoslav
作者单位：Zuse Institute Berlin; Comenius University Bratislava
摘要：Let the design of an experiment be represented by an s-dimensional vector w of weights with nonnegative components. Let the quality of w for the estimation of the parameters of the statistical model be measured by the criterion of D-optimality, defined as the mth root of the determinant of the information matrix M(w) = Sigma(s)(i=1) w(i)A(i)A(i)(T), where A(i), i = 1, ... , s are known matrices with in rows. In this paper, we show that the criterion of D-optimality is second-order cone represe...
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作者：Dette, Holger; Melas, Viatcheslav B.; Guchenko, Roman
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs...
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作者：Gao, Chao; Ma, Zongming; Ren, Zhao; Zhou, Harrison H.
作者单位：Yale University; University of Pennsylvania; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high-dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high-dimensional applications involving massive data sets. However, there has been few theoreti...
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作者：Jiang, Ci-Ren; Wang, Jane-Ling
作者单位：Academia Sinica - Taiwan; University of California System; University of California Davis
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作者：Chan, Hock Peng; Walther, Guenther
作者单位：National University of Singapore; Stanford University
摘要：We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the sparseness of the signa...
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作者：Chen, Yen-Chi; Genovese, Christopher R.; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：The large sample theory of estimators for density modes is well understood. In this paper we consider density ridges, which are a higher-dimensional extension of modes. Modes correspond to zero-dimensional, local high-density regions in point clouds. Density ridges correspond to s-dimensional, local high-density regions in point clouds. We establish three main results. First we show that under appropriate regularity conditions, the local variation of the estimated ridge can be approximated by ...
