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作者：Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
作者单位：University of Rome Tor Vergata; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called needlets. We establish a minimax result and prove its optimality. We are motivated by astrophysical applications, in particular in connection with the analysis of ultra high-energy cosmic rays.
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作者：Tokdar, Surya T.; Martin, Ryan; Ghosh, Jayanta K.
作者单位：Carnegie Mellon University; Purdue University System; Purdue University; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：Mixture models have received considerable attention recently and Newton [Sankhya Ser A 64 (2002) 306-322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over permutations of the data se...
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作者：Zhou, Zhou; Wu, Wei Biao
作者单位：University of Chicago
摘要：We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important problem raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.
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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...
