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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：Low, Mark G.; Ma, Zongming
作者单位：University of Pennsylvania
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作者：Klopp, Olga; Pensky, Marianna
作者单位：Universite Paris Saclay; State University System of Florida; University of Central Florida
摘要：The objective of the present paper is to develop a minimax theory for the varying coefficient model in a nonasymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time-dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and construct an adapti...
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作者：Levrard, Clement
作者单位：Inria
摘要：Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of O(1/n), where n is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron. J. Stat. 7 (2013) 1716-1746]. This rate is attained for the empirical risk minimizer strategy, if the source distribution satisfies some regularity conditions. However, the dependency of the average distortion on other parameters is not known, and these results are only ...
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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：Hu, Linwei; Yang, Min; Stufken, John
作者单位：University System of Georgia; University of Georgia; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Arizona State University; Arizona State University-Tempe
摘要：We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stuficen [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and...
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作者：Todorov, Viktor
作者单位：Northwestern University
摘要：We derive a nonparametric estimator of the jump-activity index beta of a locally-stable pure-jump Ito semimartingale from discrete observations of the process on a fixed time interval with mesh of the observation grid shrinking to zero. The estimator is based on the empirical characteristic function of the increments of the process scaled by local power variations formed from blocks of increments spanning shrinking time intervals preceding the increments to be scaled. The scaling serves two pu...
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作者：Fougeres, Anne-Laure; de Haan, Laurens; Mercadier, Cecile
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang [Statistics of bivariate extremes (1...
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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...
