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作者：Marchetti, Giovanni M.; Wermuth, Nanny
作者单位：University of Florence; Chalmers University of Technology
摘要：For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs i...
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作者：Wang, Huixia Judy; Zhu, Zhongyi; Zhou, Jianhui
作者单位：North Carolina State University; University of Virginia; Fudan University
摘要：Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying coefficients. The functional coefficients are estimated by basis function approximations. The estimation procedure is easy to implement, and it requires no specification of the error distributions. The asymptotic properties of the proposed estimators are established for...
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作者：Yajima, Yoshihiro; Matsuda, Yasumasa
作者单位：University of Tokyo; Tohoku University
摘要：We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting distributions of these test statistics under null hypotheses are always normal distributions, and they can be implemented easily for practical use. If null hypotheses are false, as the sample size goes to infinity, they diverge to infinity and consequently are consiste...
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作者：Davies, P. L.; Kovac, A.; Meise, M.
作者单位：University of Duisburg Essen; University of Bristol; Eindhoven University of Technology
摘要：In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and nonasymptotic confidence region A(n) which is defined by a set of linear in-equalities involving the values of the functions at the design points. Interest will typically center on certain simplest functions in A(n) where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on ...
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作者：Johannes, Jan
作者单位：Ruprecht Karls University Heidelberg
摘要：We consider the problem of estimating a density f(X) using a sample Y-l,....Y-n from f(Y) = f(X) star f(is an element of), where f(is an element of) is an unknown density. We assume that all additional sample is an element of(l),...,is an element of(m) from f(is an element of) is observed. Estimators of f(X) and its derivatives are constructed by using nonparametric estimators of f(X) and f(is an element of) and by applying a spectral cut-off in the Fourier domain. We derive the rate of conver...
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作者：Zhang, Tong
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We derive sharp performance bounds for least squares regression With L-1 regularization front parameter estimation accuracy and feature selection quality perspectives. The main result proved for L-1 regularization extends it similar result in [Ann. Statist. 35 (2007) 2313-2351] for the Dantzig selector. It gives an affirmative answer to an open question in [Ann. Statist. 35 (2007) 2358-2364]. Moreover, the result leads to an extended view of feature selection that allows less restrictive condi...
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作者：Dudley, R. M.; Sidenk, Sergiy; Wang, Zuoqin
作者单位：Massachusetts Institute of Technology (MIT); Johns Hopkins University
摘要：The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector mu and scatter matrix Sigma of an elliptically symmetric t distribution off R-d with degrees of freedom nu > 1 extends to an M-functional defined off all probability distributions P in a weakly open, weakly dense domain U. Here U consists of P Putting not too much mass in hyperplanes of dimension < d, as shown for em...
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作者：Chan, Yao-Ban; Hall, Peter
作者单位：University of Melbourne
摘要：We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of heavy-tailed data. Empirical rules are suggested for choosing the threshold. They require the bare minimum of data only one data vector is needed from each population. Theoretical and numerical aspects of performance are explored, paying particular attention to the ...
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作者：Hall, Peter; Miller, Hugh
作者单位：University of Melbourne
摘要：The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the first of these examples, the number, p, of quantities being ordered is sometimes only moderate in sire; in the second it can be very large, often much greater than sample sire. However, we show that in both types of problem the conventional bootstrap can prod...
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作者：Lv, Jinchi; Fan, Yingying
作者单位：University of Southern California
摘要：Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares estimator enjoys a nonasymptotic property, called the weak oracle property, where the dimensionality can grow exponentially with sample size. Fo...
