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作者：Fromont, Magalie; Laurent, Beatrice; Reynaud-Bouret, Patricia
作者单位：Universite de Rennes; Universite Rennes 2; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose testing procedures whose test statistics are U -statistics based on single kernel functions. The corresponding critical values are constructed from a nonasymptotic wild bootstrap approach, leading to level alpha tests. Various choices for the kernel functions are possible, including projection, approximation or reproducing kernels. In this last case, we o...
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作者：Bacallado, Sergio; Favaro, Stefano; Trippa, Lorenzo
作者单位：Stanford University; University of Turin; Collegio Carlo Alberto; Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard University Medical Affiliates; Dana-Farber Cancer Institute
摘要：We introduce a three-parameter random walk with reinforcement, called the (theta, alpha, beta) scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter beta smoothly tunes the (theta, alpha, beta) scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters a and theta modulate how many states are typically visited. Resorting to de Finetti's theorem for Markov chains, we use th...
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作者：Chung, EunYi; Romano, Joseph P.
作者单位：Stanford University; Stanford University
摘要：Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P = Q. On the other hand, when comparing or testing particular parameters theta of P and Q, such as their means or medians, permutation tests need not be level a, or even approximately level alpha in large samples. Under very weak assumptions for comparing estimators, we provide a general test procedure whereby the asymptotic validity of the permutation test...
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作者：Koltchinskii, Vladimir; Rangel, Pedro
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let (V, A) be a weighted graph with a finite vertex set V, with a symmetric matrix of nonnegative weights A and with Laplacian Delta. Let S-* : V x V bar right arrow R be a symmetric kernel defined on the vertex set V. Consider n i.i.d. observations (X-j, X'(j), Y-j), j = 1, ..., n, where X-j, X'(j) are independent random vertices sampled from the uniform distribution in V and Y-j is an element of R is a real valued response variable such that E(Y-j vertical bar X-j, X'(j)) = S-*(X-j,X'(j)), j...
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作者：Ma, Zongming
作者单位：University of Pennsylvania
摘要：Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of features p is comparable to, or even much larger than, the sample size n. In this paper, we propose a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse. Under a spiked covariance model, w...
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作者：Duchi, John C.; Mackey, Lester; Jordan, Michael I.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Stanford University
摘要：We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and more practical appro...
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作者：Huang, Jian; Sun, Tingni; Ying, Zhiliang; Yu, Yi; Zhang, Cun-Hui
作者单位：University of Iowa; University of Pennsylvania; Columbia University; Fudan University; Rutgers University System; Rutgers University New Brunswick
摘要：We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. How...
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作者：Tang, Minh; Sussman, Daniel L.; Priebe, Carey E.
作者单位：Johns Hopkins University
摘要：In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function kappa, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classification where the link function kappa belongs to the class of universal kernels and class labels are observed for a number of vertices tending to infinity and that the remaini...
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作者：Bigot, Jeremie; Gendre, Xavier
作者单位：Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of Frechet mean that is a generalization of the standard notion of averaging to non-Euclidean spaces. We derive a minimax rate for this estimation problem, and we show that our estimator achieves this optimal rate under the asymptotics where both the number of curve...
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作者：Davidov, Ori; Peddada, Shyamal
作者单位：University of Haifa; National Institutes of Health (NIH) - USA; NIH National Institute of Environmental Health Sciences (NIEHS)
摘要：Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not be ideal for testing for. order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates t...
