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作者：Wu, WB
作者单位：University of Chicago
摘要：We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations of empirical processes are discussed. Applications to the trimmed and Winsorized means are given. Our results extend previous ones by establishing sharper bounds under milder conditions and thus provide new insight into the theory of empirical processes for dependent random variables.
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作者：Bhattacharya, R; Patrangenaru, V
作者单位：University of Arizona; Texas Tech University System; Texas Tech University
摘要：This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on Riemannian manifolds. Central limit theorems are also obtained for extrinsic sample means w.r.t. an arbitrary embedding of a differentiable manifold in a Euclidean space. Bootstrap methods particularly suitable for these problems are presented. Ap...
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作者：He, XM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
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作者：Marinucci, D; Piccioni, M
作者单位：University of Rome Tor Vergata; Sapienza University Rome
摘要：We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation.
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作者：Kolaczyk, ED; Nowak, RD
作者单位：Boston University; University of Wisconsin System; University of Wisconsin Madison
摘要：We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L-2 function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy to those underlying...
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作者：Hunter, DR
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The Bradley-Terry model for paired comparisons is a simple and much-studied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among the many studies of the model in the past 75 years, numerous authors have generalized it in several directions, sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations. Building on a theory of algorithms known by the initials MM, for minorizatio...
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作者：Lang, JB
作者单位：University of Iowa
摘要：A unified approach to maximum likelihood inference for a broad, new class of contingency table models is presented. The model class comprises multinomial-Poisson homogeneous (MPH) models, which can be characterized by an independent sampling plan and a system of homogeneous constraints, h(m) - 0, where m is the vector of expected table counts. Maximum likelihood (ML) fitting and large-sample inference for MPH models are described. The MPH models are partitioned into well-defined equivalence cl...
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作者：Tsybakov, AB
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：Classification can be considered as nonparametric estimation of sets, where the risk is defined by means of a specific distance between sets associated with misclassification error. It is shown that the rates of convergence of classifiers depend on two parameters: the complexity of the class of candidate sets and the margin parameter. The dependence is explicitly given, indicating that optimal fast rates approaching O (n(-1)) can be attained, where n is the sample size, and that the proposed c...
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作者：Zhang, T
作者单位：International Business Machines (IBM); IBM USA
摘要：We study how closely the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. We show that such a classification scheme can be generally regarded as a (nonmaximum-likelihood) conditional in-class probability estimate, and we use this analysis to compare various convex loss...
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作者：Cook, RD; Bing, L
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The central mean subspace (CMS) and iterative Hessian transformation (IHT) have been introduced recently for dimension reduction when the conditional mean is of interest. Suppose that X is a vector-valued predictor and Y is a scalar response. The basic problem is to find a lower-dimensional predictor n(T)X such that E(Y\X) = E(Y\n(T)X). The CMS defines the inferential object for this problem and IHT provides an estimating procedure. Compared with other methods, IHT requires fewer assumptions a...
