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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...
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作者：Shalizi, Cosma Rohilla; Rinaldo, Alessandro
作者单位：Carnegie Mellon University
摘要：The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stocha...
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作者：Onatski, Alexei; Moreira, Marcelo J.; Hallin, Marc
作者单位：University of Cambridge; Getulio Vargas Foundation; Universite Libre de Bruxelles
摘要：This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold...
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作者：Van de Geer, Sara; Buehlmann, Peter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the problem of regularized maximum likelihood estimation for the structure and parameters of a high-dimensional, sparse directed acyclic graphical (DAG) model with Gaussian distribution, or equivalently, of a Gaussian structural equation model. We show that the to-penalized maximum likelihood estimator of a DAG has about the same number of edges as the minimal-edge I-MAP (a DAG with minimal number of edges representing the distribution), and that it converges in Frobenius norm. We ...
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作者：Saegusa, Takumi; Wellner, Jon A.
作者单位：University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
摘要：We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko-Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling and sampling without replacement at the se...
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作者：Kato, Kengo
作者单位：University of Tokyo
摘要：This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional assumption on the data generating process, we consider a quasi-likelihood induced from the conditional moment restriction, and put priors on the function-valued parameter. We call the resulting posterior quasi-posterior, which corresponds to Gibbs posterior in th...
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作者：Xie, Yao; Siegmund, David
作者单位：Duke University; Stanford University
摘要：We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream specific generalized likeli...
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作者：Chan, Hock Peng; Lai, Tze Leung
作者单位：National University of Singapore; Stanford University
摘要：By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.
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作者：Schennach, Susanne M.
作者单位：Brown University
摘要：This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These examples illustrate t...
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作者：Liu, Weidong; Shao, Qi-Man
作者单位：Shanghai Jiao Tong University; Chinese University of Hong Kong
摘要：A Cramer moderate deviation theorem for Hotelling's T-2-statistic is proved under a finite (3 + delta)th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as large as e(0)(n(1/3)) before the chi-squared distribution calibration becomes inaccurate. As an application of the moderate deviation results, a global test on the equality of m mean vectors based on the maximum of Hotelling's T-2-statistics is developed and its...
