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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, ...
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作者：Chen, Dong; Hall, Peter; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis; University of Melbourne
摘要：Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional functions. This difficulty has led to an emphasis on the so-called functional linear model, which is much more flexible than common linear models in finite dimension, but nevertheless imposes structural constraints on the relationship between predictors and res...
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作者：Levy-Leduc, C.; Boistard, H.; Moulines, E.; Taqqu, M. S.; Reisen, V. A.
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 1 Capitole; Toulouse School of Economics; Boston University; Universidade Federal do Espirito Santo
摘要：Let (Xi)(i >= 1) be a stationary mean-zero Gaussian process with covariances rho(k) = E(X-1 Xk+1) satisfying rho(0) = 1 and rho(k) = k(-D) L(k), where D is in (0, 1), and L is slowly varying at infinity. Consider the U-process {U-n(r), r is an element of 1} defined as U-n(r) = 1/n (n-1) Sigma(1 <= i not equal j <= n) 1{G(X-i, X-j)<= r} where I is an interval included in R, and G is a symmetric function. In this paper, we provide central and noncentral limit theorems for U-n. They are used to d...
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作者：Shao, Jun; Wang, Yazhen; Deng, Xinwei; Wang, Sijian
作者单位：East China Normal University; University of Wisconsin System; University of Wisconsin Madison
摘要：In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is usually unknown, the rule of classification is constructed using a training sample. The well-known linear discriminant analysis (LDA) works well for the situation where the number of variables used for classification is much smaller than the training sample s...
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作者：Kneip, Alois; Sarda, Pascal
作者单位：University of Bonn; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach: it is assumed that the predictor vector can be decomposed into a sum of two uncorrelated random components reflecting common factors and specific variabilities of the explanatory variables. It is shown that the traditional assumpt...
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作者：McCullagh, Peter; Han, Han
作者单位：University of Chicago
摘要：Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that all priors be proper. This paper begins with the observation that an improper measure on 8 satisfying K...
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作者：Haff, L. R.; Kim, P. T.; Koo, J. -Y.; Richards, D. St P.
作者单位：University of California System; University of California San Diego; University of Guelph; Korea University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or non...
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作者：Maruyama, Yuzo; George, Edward I.
作者单位：University of Tokyo; University of Pennsylvania
摘要：For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner's g-prior which allows for p > n. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.
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作者：Meister, Alexander
作者单位：University of Rostock
摘要：We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam's sense under known design distribution. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes. As an application, w...
