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作者：Bickel, Peter J.; Chen, Aiyou; Levina, Elizaveta
作者单位：University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated; University of Michigan System; University of Michigan
摘要：Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average...
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作者：Hall, Peter; Tung Pham; Wand, M. P.; Wang, S. S. J.
作者单位：University of Melbourne; University of Wollongong; University of Technology Sydney
摘要：We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and...
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作者：Ilmonen, Pauliina; Paindaveine, Davy
作者单位：Aalto University; Universite Libre de Bruxelles; Universite Libre de Bruxelles; Tampere University; Sorbonne Universite
摘要：We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = Lambda Z + mu, where mu is a p-vector, Lambda is a full-rank p x p matrix and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Lambda. On the basis of n i.i.d. copies of X, we develop, under a sym...
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作者：Audibert, Jean-Yves; Catoni, Olivier
作者单位：Universite Gustave-Eiffel; ESIEE Paris; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the problem of robustly predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For the ridge estimator and the ordinary least squares estimator, and their variants, we provide new risk bounds of order d/n without logarithmic factor unlike some standard results, where n is the size of the training data. We also provide a new estimator with bett...
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作者：Rojo, Javier
作者单位：Rice University
摘要：Through the use of a system-building approach, an approach that includes finding common ground for the various philosophical paradigms within statistics, Erich L. Lehmann is responsible for much of the synthesis of classical statistical knowledge that developed from the Neyman-Pearson-Wald school. A biographical sketch and a brief summary of some of his many contributions are presented here. His complete bibliography is also included and the references present many other sources of information...
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作者：van Zwet, Willem R.
作者单位：Leiden University; Leiden University - Excl LUMC
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作者：Buta, Eugenia; Doss, Hani
作者单位：Yale University; State University System of Florida; University of Florida
摘要：We consider situations in Bayesian analysis where we have a family of priors v(h) on the parameter theta, where h varies continuously over a space H, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of theta. How do we efficiently estimate the posterior expectation of f(theta) simultaneously for all h in H? The second problem is how do we identify subsets of H which give rise to reasonable choices of v(h)? We a...
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作者：Buhlmann, Peter; Cai, Tony
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Pennsylvania
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作者：Lerman, Gilad; Zhang, Teng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p > 0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l(p)-averaged distances of the sampled data points from any K subspaces. Under some conditions, we show that if 0 < p <= 1, then all underlying subspaces can be precisely recovered by l(p) minimization with overwhelming probability. On the other hand, i...
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作者：Nye, Tom M. W.
作者单位：Newcastle University - UK
摘要：Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary trees on a fixed set of taxa is not a vector space. This paper describes a novel geometrical approach to PCA in tree-space that constructs the first principal path in an analogous way to standard linear Euclidean PCA. Given a data set of phylogenetic trees, ...
