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作者：Huang, Junzhou; Zhang, Tong
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
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作者：Xue, Hongqi; Miao, Hongyu; Wu, Hulin
作者单位：University of Rochester
摘要：This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurem...
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作者：Zhu, Hongjian; Hu, Feifang
作者单位：University of Virginia
摘要：Clinical trials are complex and usually involve multiple objectives such as controlling type I error rate, increasing power to detect treatment difference, assigning more patients to better treatment, and more. In literature, both response-adaptive randomization (RAR) procedures (by changing randomization procedure sequentially) and sequential monitoring (by changing analysis procedure sequentially) have been proposed to achieve these objectives to some degree. In this paper, we propose to seq...
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作者：Cai, T. Tony; Zhang, Cun-Hui; Zhou, Harrison H.
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick; Yale University
摘要：Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm. It is shown that optimal procedures under the two norms are different and consequently matrix es...
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作者：Yang, Min
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Deriving optimal designs for nonlinear models is, in general, challenging. One crucial step is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza Phenomenon states that under a (p - 1)th-degree polynomial regression model, any optimal design can be based on at most p design points, the minimum number of support points such that all p...
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作者：Bowsher, Clive G.
作者单位：University of Cambridge
摘要：The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition [A, D, B]...
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作者：Huang, Jian; Horowitz, Joel L.; Wei, Fengrong
作者单位：University of Iowa; Northwestern University; University System of Georgia; University of West Georgia
摘要：We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is small relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of ...
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作者：Bigot, Jeremie; Gadat, Sebastien
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role of a convolution operator. An adaptive estimator of the mean pattern, based on wavelet thresholding is proposed. We study its consistency for the quadratic risk as the number of observed curves tends to infinity, and this estimator is shown to achieve a near-...
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作者：Sen, Bodhisattva; Banerjee, Moulinath; Woodroofe, Michael
作者单位：Columbia University; University of Michigan System; University of Michigan
摘要：In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n(1/3). The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0, infinity), is a prototypical example. We focus on this example and explore different approaches to constructing bootstrap confidence intervals for f(t(0)), where t(o) is an element of (0, infinit...
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作者：Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.; Barbu, Adrian
作者单位：State University System of Florida; Florida State University; Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：This paper studies sparse density estimation via l(1) penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. We offer a data driven method ...
