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作者：Juditsky, Anatoli B.; Lepski, Oleg V.; Tsybakov, Alexandre B.
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Aix-Marseille Universite; Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Cite; Sorbonne Universite
摘要：We study the problem of nonparametric estimation of a multivariate function g: R-d -> R that can be represented as a composition of two unknown smooth functions f : R -> R and G :R-d -> R. We suppose that f and G belong to known smoothness classes of functions, with smoothness gamma and beta, respectively. We obtain the full description of minimax rates of estimation of g in terms of gamma and beta, and propose rate-optimal estimators for the sup-norm loss. For the construction of such estimat...
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作者：VanderWeele, Tyler J.; Robins, James M.
作者单位：University of Chicago; Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard T.H. Chan School of Public Health
摘要：Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs. This in turn provides a clear theoretical link between two major conceptualizations of causality: one counterfactual-based and the other based on a more mechanistic understanding o...
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作者：Maathuis, Marloes H.; Kalisch, Markus; Buehlmann, Peter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of t...
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作者：Berger, James O.; Bernardo, Jose M.; Sun, Dongchu
作者单位：Duke University; University of Missouri System; University of Missouri Columbia
摘要：Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an ex...
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作者：May, Caterina; Flournoy, Nancy
作者单位：University of Milan; University of Eastern Piedmont Amedeo Avogadro; University of Missouri System; University of Missouri Columbia
摘要：This paper illustrates asymptotic properties for a response-adaptive design generated by a two-color, randomly reinforced urn model. The design considered is optimal in the sense that it assigns patients to the best treatment, with probability converging to one. An approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one. Results on the rate of convergence of t...
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作者：Xie, Huiliang; Huang, Jian
作者单位：University of Miami; University of Iowa
摘要：We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneou...
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作者：Leeb, Hannes
作者单位：Yale University
摘要：We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite, where no regularity conditions are imposed on unknown parameters, where the number of explanatory variables in a good model can be of the same order as sample size and where the number of candidate models can be of larger order t...
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作者：Singh, Aarti; Scott, Clayton; Nowak, Robert
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Michigan System; University of Michigan
摘要：Consider the problem of estimating the gamma-level set G(gamma)* = {x : f(x) > gamma} of an unknown d-dimensional density function f based on n independent observations X(1), ..., X(n) from the density. This problem has been addressed under global error criteria related to the symmetric set difference. However, in certain applications a spatially uniform mode of convergence is desirable to ensure that the estimated set is close to the target set everywhere. The Hausdorff error criterion provid...
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作者：Bickel, Peter J.; Ritov, Ya'acov; Tsybakov, Alexandre B.
作者单位：University of California System; University of California Berkeley; Hebrew University of Jerusalem; Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. Forboth methods, wederive, inparallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the e(p) estimation loss for 1 <= p <= 2 in the linear model when the number of variables can be Much larger than the sample size.
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作者：Chen, Hegang H.; Cheng, Ching-Shui
作者单位：University System of Maryland; University of Maryland Baltimore; University of California System; University of California Berkeley
摘要：It is known that all resolution IV regular 2(n-m) designs of run size N = 2(n-m) where 5N/16 < n < N/2 must be projections of the maximal even design with N/2 factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even 2(n-m) design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration 2(n-m) designs of resolution IV and the structures of their com...
