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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...
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作者：Nickl, Richard; van de Geer, Sara
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The problem of constructing confidence sets in the high-dimensional linear model with n response variables and p parameters, possibly p >= n, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed n(-1/4), otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity leve...
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作者：He, Yangbo; Jia, Jinzhu; Yu, Bin
作者单位：Peking University; Peking University; University of California System; University of California Berkeley
摘要：Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov cha...
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作者：Hong, Yongmiao; Lee, Yoon-Jin
作者单位：Cornell University; Cornell University; Xiamen University; Xiamen University; Indiana University System; Indiana University Bloomington
摘要：The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable nonparametric inference procedure. In this paper, we show that although it inherits many advantages of the parametric maximum likelihood ratio (LR) test, the GLR test does not have the optimal power property. We propose a generally applicable test based on loss funct...
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作者：Cai, T. Tony; Low, Mark G.; Xia, Yin
作者单位：University of Pennsylvania
摘要：Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchmarks show that the constructed confidence intervals have near minimum expected length for each indivi...
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作者：Khmaladze, Estate
作者单位：Victoria University Wellington
摘要：The paper proposes one-to-one transformation of the vector of components {Y-in}(i=1)(m) of Pearson's chi-square statistic, Y-in = nu(in)-npi/root np(i,) i = l, ... , m, into another vector {Z(in)}(i=1)(m), which, therefore, contains the same statistical information, but is asymptotically distribution free. Hence any functional/test statistic based on {Z(in)}(i=1)(m) is also asymptotically distribution free. Natural examples of such test statistics are traditional goodness-of-fit statistics fro...
