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作者：Qian, Peter Z. G.; Ai, Mingyao; Wu, C. F. Jeff
作者单位：University of Wisconsin System; University of Wisconsin Madison; Peking University; University System of Georgia; Georgia Institute of Technology
摘要：New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing Such designs. The development of these methods also leads to the introduction of several new discrete mathematics concepts, including nested orthogonal arrays and nested difference matrices.
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作者：Gavrilov, Yulia; Benjamini, Yoav; Sarkar, Sanat K.
作者单位：Tel Aviv University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m + 1 - i (1 - q)], i = 1,..., m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses. We prove...
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作者：Hall, Peter; Mueller, Hans-Georg; Yao, Fang
作者单位：University of Melbourne; University of California System; University of California Davis; University of Toronto
摘要：Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the nature of the functional relationship, we aim to estimate the directional derivatives and gradients of the response with respect to the predictor functions. In statistical applications and data analysis, functional derivatives provide a quantitative measure o...
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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...
