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作者：Fan, Jianqing; Fan, Yingying; Barut, Emre
作者单位：Princeton University; University of Southern California; International Business Machines (IBM); IBM USA
摘要：Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L-1-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L-1-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size,...
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作者：Bochkina, Natalia A.; Green, Peter J.
作者单位：University of Edinburgh; University of Bristol; University of Technology Sydney
摘要：We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the true solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and that the posterior distribution has not only Gaussian components as in the case of regular models (the Bernstein-von Mises theorem) but also has Gamma distribution components whose form depends on the behaviour of the prior distribution near the boundary and h...
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作者：Castillo, Ismael
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when strong measures of distances, such as the sup-norm, are considered. In particular, we show that likelihood methods can achieve optimal minimax sup-norm rates in density estimation on the unit interval. The introduced methodology is used to prove that commonly used families of prior distributions on densities, namely log-density pri...
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作者：Bhattacharya, Anirban; Pati, Debdeep; Dunson, David
作者单位：Texas A&M University System; Texas A&M University College Station; State University System of Florida; Florida State University; Duke University
摘要：In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a Gaussian process prior...
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作者：Luo, Wei; Li, Bing; Yin, Xiangrong
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University System of Georgia; University of Georgia
摘要：We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the ...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in other words, performing least squares under a convex constraint. Many problems in modern statistics and statistical signal processing theory are special cases of this general situation. Examples include the lasso and other high-dimensional regression techniq...
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作者：Groeneboom, Piet
作者单位：Delft University of Technology
摘要：We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show that, under smoothness conditions on the underlying distributions and using the usual bandwidth choice in density estimation, the local convergence rate is n(-2/5) and the limit distribution is normal, in contrast with the rate n(-1/3) of the ordinary maxim...
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作者：Shi, Ce; Tang, Yu; Yin, Jianxing
作者单位：Soochow University - China
摘要：As a type of search design, a detecting array can be used to generate test suites to identify and detect faults caused by interactions of factors in a component-based system. Recently, the construction and optimality of detecting arrays have been investigated in depth in the case where all the factors are assumed to have the same number of levels. However, for real world applications, it is more desirable to use detecting arrays in which the various factors may have different numbers of levels...
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作者：Lockhart, Richard; Taylor, Jonathan; Tibshirani, Ryan J.; Tibshirani, Robert
作者单位：Simon Fraser University; Stanford University; Carnegie Mellon University; Stanford University
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作者：Bailey, R. A.; Druilhet, P.
作者单位：University of London; Queen Mary University London; University of St Andrews; Universite Clermont Auvergne (UCA)
摘要：We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carryover and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient...
