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作者：Caron, Francois; Fox, Emily B.
作者单位：University of Oxford; University of Washington; University of Washington Seattle
摘要：Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this arraywhich can aid in modelling, computations and theoretical analysisthe Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely rand...
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作者：Gourieroux, Christian; Zakoian, Jean-Michel
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Toronto; Universite de Lille
摘要：The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such mode...
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作者：Brockwell, Peter J.; Matsuda, Yasumasa
作者单位：Colorado State University System; Colorado State University Fort Collins; Tohoku University
摘要：We define an isotropic Levy-driven continuous auto-regressive moving average CARMA(p,q) random field on Rn as the integral of a radial CARMA kernel with respect to a Levy sheet. Such fields constitute a parametric family characterized by an auto-regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half-planes. They extend the well-balanced Ornstein-Uhlenbeck process of Schnurr and Woerner to a well-balanced CARMA process in one dimension...
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作者：Wadsworth, J. L.; Tawn, J. A.; Davison, A. C.; Elton, D. M.
作者单位：Lancaster University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either appli...
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作者：Comte, Fabienne; Cuenod, Charles-A.; Pensky, Marianna; Rozenholc, Yves
作者单位：Universite Paris Cite; Assistance Publique Hopitaux Paris (APHP); Universite Paris Cite; Hopital Universitaire Europeen Georges-Pompidou - APHP; State University System of Florida; University of Central Florida
摘要：We consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of linear equations with the matrix...
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作者：Cannings, Timothy I.; Samworth, Richard J.
作者单位：University of Cambridge
摘要：We introduce a very general method for high dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower dimensional space. In one special case that we study in detail, the random projections are divided into disjoint groups, and within each group we select the projection yielding the smallest estimate of the test error. Our random-projection ensemble classifier then aggregates the res...
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作者：Zwiernik, Piotr; Uhler, Caroline; Richards, Donald
作者单位：Pompeu Fabra University; Massachusetts Institute of Technology (MIT); Institute of Science & Technology - Austria; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Al...
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作者：Griffin, Jim E.; Leisen, Fabrizio
作者单位：University of Kent
摘要：A new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in Bayesian non-parametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, sigma-stable and generalized gamma process marginals. We also deriv...
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作者：Lu, Shu; Liu, Yufeng; Yin, Liang; Zhang, Kai
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built-in variable selection. The lasso is perhaps one of the most well-known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality techniques in optimization to...
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作者：Stadler, Nicolas; Mukherjee, Sach
作者单位：Netherlands Cancer Institute; Helmholtz Association; German Center for Neurodegenerative Diseases (DZNE)
摘要：We propose new methodology for two-sample testing in high dimensional models. The methodology provides a high dimensional analogue to the classical likelihood ratio test and is applicable to essentially any model class where sparse estimation is feasible. Sparse structure is used in the construction of the test statistic. In the general case, testing then involves non-nested model comparison, and we provide asymptotic results for the high dimensional setting. We put forward computationally eff...
