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作者：Einmahl, John H. J.; Segers, Johan
作者单位：Tilburg University; Universite Catholique Louvain
摘要：Consider a random sample from a bivariate distribution function F in the max-domain of attraction of all extreme-value distribution function G. This G is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of F. A major issue in multivariate extreme-value theory is the estimation of the spectral measure (1)p with respect to the L-p norm. For every p is an element of [1, infinity], a nonparametric maximum empirical likelihood e...
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作者：Genest, Christian; Segers, Johan
作者单位：Laval University; Universite Catholique Louvain; Tilburg University
摘要：Consider a continuous random pair (X, Y) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859-878.] and Caperaa, Fougeres and Genest [Biometrika 84 (1997) 567-577]. In this paper, rank-based versions of these estimators are proposed for the mo...
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作者：Balabdaoui, Fadoua; Rufibach, Kaspar; Wellner, Jon A.
作者单位：Universite PSL; Universite Paris-Dauphine; University of Zurich; University of Washington; University of Washington Seattle; University of Gottingen
摘要：We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form f(0) = exp phi(0) where phi(0) is a concave function on R. The pointwise limiting distributions depend on the second and third derivatives at 0 of H-k, the lower invelope of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of phi(0) = log f(0) at the point of interest. We also establish the limit...
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作者：Paul, Debashis; Peng, Jie
作者单位：University of California System; University of California Davis
摘要：[it this paper we consider two closely related problems: estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In [A geometric approach to maximum likelihood estimation of covariance kernel from sparse irregular longitudinal data (2007)], a restricted maximum likelihood (REML) approach has b...
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作者：Nussbaum, Michael; Szkola, Arleta
作者单位：Cornell University; Max Planck Society
摘要：We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the asymptotic rate exponents of Bayesian error probabilities. The bound represents a quantum extension of the Chernoff bound, which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set. In ...
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作者：Liu, Jiawei; Lindsay, Bruce G.
作者单位：University System of Georgia; Georgia State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We introduce a semiparametric tubular neighborhood of a parametric model in the multinomial setting. It consists of all multinomial distributions lying in a distance-based neighborhood of the parametric model of interest. Fitting such a tubular model allows one to use a parametric model while treating it as an approximation to the true distribution. In this paper, the Kullback-Leibler distance is used to build the tubular region. Based on this idea one can define the distance between the true ...
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作者：Ali, R. Ayesha; Richardson, Thomas S.; Spirtes, Peter
作者单位：University of Guelph; University of Washington; University of Washington Seattle; Carnegie Mellon University
摘要：Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We state and prove conditions under which two maximal ancestral graphs are Markov equivalent to each other, thereby extending analogous results for DAGs given by other authors. These conditions lead to an algorithm for determining Markov equivale...
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作者：Phoa, Frederick K. H.; Xu, Hongquan
作者单位：University of California System; University of California Los Angeles
摘要：The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191-1213] suggested a new class of nonregular designs Constructed from quaternary codes. This paper explores the properties and uses Of quaternary codes toward the construction of quarter-fraction nonregular designs. Some theoretical results are obtained regarding the aliasing structure Of Such desig...
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作者：Hsing, Tailen; Ren, Haobo
作者单位：University of Michigan System; University of Michigan; Sanofi-Aventis; Sanofi USA
摘要：Suppose that Y is a scalar and X is a second-order stochastic process, where Y and X are conditionally independent given the random variables xi(1), ..., xi(p) which belong to the closed span L-X(2) of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of L-X(2) with the reproducing kernel Hilbert space of X provides a platform for a seamless extension from the finite- to infinite-dimensional settings. It a...
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作者：Chen, Xiaohong; Wu, Wei Biao; Yi, Yanping
作者单位：Yale University; University of Chicago; New York University
摘要：This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that M...
