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作者：Chan, Ngai Hang; Huang, Shih-Feng; Ing, Ching-Kang
作者单位：Chinese University of Hong Kong; National University Kaohsiung; Academia Sinica - Taiwan
摘要：A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction errors (MSPE) of the...
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作者：Buecher, Axel; Vetter, Mathias
作者单位：Ruhr University Bochum
摘要：In this paper nonparametric methods to assess the multivariate Levy measure are introduced. Starting from high-frequency observations of a Levy process X, we construct estimators for its tail integrals and the Pareto-Levy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length Delta(n), the rate of convergence is k(n)(-1/2) for k(n) = n Delta(n) which is natural concerning inference on the Levy measure. Besid...
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作者：Schmidt-Hieber, Johannes; Munk, Axel; Duembgen, Lutz
作者单位：Vrije Universiteit Amsterdam; University of Gottingen; Max Planck Society; University of Bern
摘要：We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investi...
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作者：Bien, Jacob; Taylor, Jonathan; Tibshirani, Robert
作者单位：Cornell University; Cornell University; Stanford University; Stanford University
摘要：We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy holds with probability one and derive an unbiased estimate for the degrees of freedom of our estimator. A bound on this estimate reveals the amount of fitting saved by the hiera...
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作者：Zhang, Xianyang; Shao, Xiaofeng
作者单位：University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based t-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new boot...
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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：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：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：Cappe, Olivier; Garivier, Aurelien; Maillard, Odalric-Ambrym; Munos, Remi; Stoltz, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Leoben; Inria; Centre National de la Recherche Scientifique (CNRS); Hautes Etudes Commerciales (HEC) Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148-177], based on upper confidence bounds of the arm payoffs computed using the Kullback-Leibler divergence. We consider two classes of distributions for which instances of this general idea are analyzed: the kl-UCB algorithm is designed for one-parameter exponential familie...
