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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：Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
作者单位：University of Rome Tor Vergata; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Cite
摘要：We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT converaence results for polynomial functionals of the ...
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作者：Chang, Hua-Hua; Ying, Zhiliang
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Columbia University
摘要：Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive design obtained by maxi...
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作者：Casella, George; Giron, F. Javier; Martinez, M. Lina; Moreno, Elias
作者单位：State University System of Florida; University of Florida; Universidad de Malaga; University of Granada
摘要：It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces I consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that the asymptotics of...
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作者：Arias-Castro, Ery; Donoho, David L.
作者单位：University of California System; University of California San Diego; Stanford University
摘要：Image processing researchers commonly assert that median filtering is better than linear filtering for removing noise in the presence of edges. Using a straightforward large-n decision-theory framework, this folk-theorem is seen to be false in general. We show that median filtering and linear filtering have similar asymptotic worst-case mean-squared error (MSE) when the signal-to-noise ratio (SNR) is of order 1, which corresponds to the case of constant per-pixel noise level in a digital signa...
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作者：Balakrishnan, N.; Zhao, Xingqiu
作者单位：McMaster University; Hong Kong Polytechnic University
摘要：This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. For the problem considered, we construct two new classes of nonparametric test statistics based on the accumulated weighted differences between the rates of increase of the estimated mean functions of the counting process...
