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作者：Panaretos, Victor M.; Tavakoli, Shahin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an asymptotic Gaussian repres...
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作者：Gao, Fuqing
作者单位：Wuhan University
摘要：In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied to the hypothesis testing problem and the confidence interval for the coverage.
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作者：Leeb, Hannes
作者单位：University of Vienna
摘要：We study the conditional distribution of low-dimensional projections from high-dimensional data, where the conditioning is on other low-dimensional projections. To fix ideas, consider a random d-vector Z that has a Lebesgue density and that is standardized so that EZ = 0 and EZZ' = I-d. Moreover, consider two projections defined by unit-vectors alpha and beta, namely a response y = alpha'Z and an explanatory variable x = beta'Z. It has long been known that the conditional mean of y given x is ...
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作者：Anandkumar, Animashree; Valluvan, Ragupathyraj
作者单位：University of California System; University of California Irvine
摘要：The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of correlation decay. For the special case of the Ising model, the number of samples n required for structural consistency of our method scales as n = Omega(theta(-delta eta(eta+1)-2)(m...
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作者：Lepski, Oleg
作者单位：Aix-Marseille Universite
摘要：This paper deals with the density estimation on R-d under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multivariate density model. Usefulness of the...
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作者：Ho, Lam Si Tung; Ane, Cecile
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When observations are modeled using an Ornstein-Uhlenbeck (OU) process along the tree, the autocorrelation between two tips decreases exponentially with their tree distance. These models are most often applied in evolutionary biology, when tips represent biological specie...
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作者：Azizyan, Martin; Singh, Aarti; Wasserman, Larry
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：Semisupervised methods are techniques for using labeled data (X-1, Y-1), ..., (X-n, Y-n) together with unlabeled data Xn+1, ..., X-N to make predictions. These methods invoke some assumptions that link the marginal distribution P-X of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of P-X. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a m...
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作者：Perchet, Vianney; Rigollet, Philippe
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Princeton University
摘要：We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side information is available We adopt a nonparametric model where the expected rewards are smooth functions of the covariate and where the hardness of the problem is captured by a margi...
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作者：Hilgert, Nadine; Mas, Andre; Verzelen, Nicolas
作者单位：INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier
摘要：We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional principal component analysis. Interestingly, the procedures are completely data-driven and do not require any prior knowledge on the smoothness of the slope nor on the smoothness of the covariate functions. The levels and powers against local alternatives are as...
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作者：Uhler, Caroline; Raskutti, Garvesh; Buehlmann, Peter; Yu, Bin
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Berkeley
摘要：Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In c...
