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作者：Chambaz, Antoine
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be strongly consistent. A version of Stein's lemma yields an optimal underestimation error exponent. The lemma also implies that the overestimation error exponent is necessarily trivial. Our tests admit nontrivial underestimation error exponents. The optimal underesti...
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作者：Berkes, Istvan; Horvath, Lajos; Kokoszka, Piotr; Shao, Qi-Man
作者单位：Graz University of Technology; Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; Utah State University; Utah System of Higher Education; University of Utah; University of Oregon; Hong Kong University of Science & Technology
摘要：We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly dependent with one change in mean at an unknown point, and under the alternative it is long-range dependent. We compute the CUSUM statistic T-n, which allows us to construct an estimator (k) over cap of a change-point. We then compute the statistic T-n,T-1 based o...
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作者：Davies, P. Laurie; Gather, Ursula
作者单位：University of Duisburg Essen; Dortmund University of Technology
摘要：In his discussion of Davies and Gather [Ann. Statist. 33 (2005) 977-1035] Tyler pointed out that the theory developed there could not be applied to the case of directional data. He related the breakdown of directional functionals to the problem of definability. In this addendum we provide a concept of breakdown defined in terms of definability and not in terms of bias. If a group of finite order k acts on the sample space we show that the breakdown point can be bounded above by (k - 1)/k. In t...
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作者：Gardner, Richard J.; Kiderlen, Markus; Milanfar, Peyman
作者单位：Western Washington University; Aarhus University; University of California System; University of California Santa Cruz
摘要：We investigate algorithms for reconstructing a convex body K in R-n from noisy measurements of its support function or its brightness function in k directions u(1), (. .) (.) , u(k). The key idea of these algorithms is to construct a convex polytope P-k whose support function (or brightness function) best approximates the given measurements in the directions u(1), (.) (.) (.) , u(k) (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. ...
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作者：Coram, Marc; Lalley, Steven P.
作者单位：University of Chicago
摘要：do nonparametric Bayesian procedures overfit? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let v be any probability distribution on the nonnegative integers. To sample a function f from the prior pi(v), first sample m from v and then sample f uniformly from the set of step functions from [0,...
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作者：Goldenshluger, Alexander; Zeevi, Assaf
作者单位：University of Haifa; Columbia University
摘要：We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane ...
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作者：Mei, Yajun
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：The purpose of this note is to show that in a widely cited paper by Yakir [Ann. Statist. 25 (1997) 2117-2126], the proof that the so-called modified Shiryayev-Roberts procedure is exactly optimal is incorrect. We also clarify the issues involved by both mathematical arguments and a simulation study. The correctness of the theorem remains in doubt.
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作者：Dahlhaus, Rainer; Rao, Suhasini Subba
作者单位：Ruprecht Karls University Heidelberg
摘要：In this paper the class of ARCH(infinity) models is generalized to the nonstationary class of ARCH(infinity) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation locally stationary ARCH(infinity) process. The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < infinity) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the proc...
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作者：Hall, Peter; Mueller, Hans-Georg; Wang, Jane-Ling
作者单位：Australian National University; University of California System; University of California Davis
摘要：The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of functional data analysis, it has often been assumed that a sample of random functions is observed precisely, in the continuum and without noise. While this has been the traditional setting for functional data analysis, in the context of longitudinal data analysis a random function typically represents a patient, or subject, who is observed at only a small number...
