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作者：Cai, T. Tony; Guo, Zijian
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
摘要：This paper considers point and interval estimation of the l(q) loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the l(q) loss and the minimax expected length of confidence intervals for the l(q) loss of rate-optimal estimators of the regression vector, including commonly used estimators such as Lasso, scaled Lasso, square-root Lasso and Dantzig Selector. Adaptivity of confidence intervals for the l(q) loss is also studi...
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作者：Hirose, Masayo Yoshimori; Lahiri, Partha
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University System of Maryland; University of Maryland College Park
摘要：The two-level normal hierarchical model (NHM) has played a critical role in statistical theory for the last several decades. In this paper, we propose random effects variance estimator that simultaneously (i) improves on the estimation of the related shrinkage factors, (ii) protects empirical best linear unbiased predictors (EBLUP) [same as empirical Bayes (EB)] of the random effects from the common overshrinkage problem, (iii) avoids complex bias correction in generating strictly positive sec...
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作者：Elenberg, Ethan R.; Khanna, Rajiv; Dimakis, Alexandros G.; Negahban, Sahand
作者单位：University of Texas System; University of Texas Austin; Yale University
摘要：We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe [In ICML (2011) 1057-1064] from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this connection allows us to obtain strong multiplicative performance bounds on several methods without statistical modeling assumptions. We also derive recovery guarantees of this form under standard assumptions. Our work shows that greedy algorithm...
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作者：Gu, Mengyang; Wang, Xiaojing; Berger, James O.
作者单位：Johns Hopkins University; University of Connecticut; Duke University
摘要：We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive. The posterior modes that are studied arise from...
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作者：Brouste, Alexandre; Fukasawa, Masaaki
作者单位：Le Mans Universite; University of Osaka
摘要：Local Asymptotic Normality (LAN) property for fractional Gaussian noise under high-frequency observations is proved with nondiagonal rate matrices depending on the parameter to be estimated. In contrast to the LAN families in the literature, nondiagonal rate matrices are inevitable. As consequences of the LAN property, a maximum likelihood sequence of estimators is shown to be asymptotically efficient and the likelihood ratio test on the Hurst parameter is shown to be an asymptotically uniform...
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作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Tong Tong
作者单位：Southwestern University of Finance & Economics - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Rochester
摘要：Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations for flexibly and adaptively incorporating data information. It is known that EL approaches encounter difficulties when dealing with high-dimensional problems. To overcome the challenges, we begin our study with investigating high-dimensional EL from a new scope targeting at high-dimensional sparse model parameters. We show that the new scope provides an opportunity...
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作者：Heinrich, Philippe; Kahn, Jonas
作者单位：Universite de Lille; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with m(0) components, the optimal local minimax rate of estimation of a mixing distribution with m components is n(-1/(4(m-m0)+2)). This corrects a previous paper by Chen [Ann. Statist. 23 (1995) 221-233]. By contrast, it turns out that there are estimators with a (nonuniform) point...
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作者：Javanmard, Adel; Montanari, Andrea
作者单位：University of Southern California; Stanford University; Stanford University
摘要：Performing statistical inference in high-dimensional models is challenging because of the lack of precise information on the distribution of high-dimensional regularized estimators. Here, we consider linear regression in the high-dimensional regime p >> n and the Lasso estimator: we would like to perform inference on the parameter vector theta*is an element of R-p. Important progress has been achieved in computing confidence intervals and p-values for single coordinates. theta(i)*, i is an ele...
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作者：Zhang, Bo; Pan, Guangming; Gao, Jiti
作者单位：Nanyang Technological University; Monash University
摘要：Let {Z(ij)} be independent and identically distributed (i.i.d.) random variables with EZ(ij) = 0, E vertical bar Z(ij)vertical bar(2) = 1 and E vertical bar Z(ij)vertical bar(4) < infinity. Define linear processes Y-tj = Sigma(infinity)(k=0) b(k) Z(t -k,j) with Sigma(infinity)(i=0) vertical bar b(i)vertical bar < infinity. Consider a p-dimensional time series model of the form x(t) = Pi x(t-1) + Sigma(1/2)y(t), 1 <= t <= T with y(t) = (Y-t(1), ..., Y-tp)' and Sigma(1/2) be the square root of a...
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作者：Sienkiewicz, Ela; Wang, Haonan
作者单位：Colorado State University System; Colorado State University Fort Collins
摘要：In this paper, we consider a set of unlabeled tree objects with topological and geometric properties. For each data object, two curve representations are developed to characterize its topological and geometric aspects. We further define the notions of topological and geometric medians as well as quantiles based on both representations. In addition, we take a novel approach to define the Pareto medians and quantiles through a multi-objective optimization problem. In particular, we study two dif...
