The Annals of Statistics

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• Explicit representation of finite predictor coefficients and its applications AI翻译
  作者：Inoue, Akihiko; Kasahara, Yukio
  作者单位：Hokkaido University
  摘要：We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.
• Discussion: Local Rademacher complexities and oracle inequalities in risk minimization AI翻译
  作者：van de Geer, Sara
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
• Resampling methods for spatial regression models under a class of stochastic designs AI翻译
  作者：Lahiri, S. N.; Zhu, Jun
  作者单位：Iowa State University; University of Wisconsin System; University of Wisconsin Madison
  摘要：In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs. A variant of the blocking mechanism is proposed. It is shown that the proposed block bootstrap method provi...
• Testing the order of a model AI翻译
  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...
• Adaptive multiscale detection of filamentary structures in a background of uniform random points AI翻译
  作者：Arias-Castro, Ery; Donoho, David L.; Huo, Xiaoming
  作者单位：University of California System; University of California San Diego; Stanford University; University System of Georgia; Georgia Institute of Technology
  摘要：We are given a set of n points that might be uniformly distributed in the unit square [0, 1](2). We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled from some (a priori unknown) curve with C-alpha-norm bounded by beta. An asymptotic detection threshold exists in this problem; for a constant T_ (alpha, beta) > 0, if the number of points sampled from the curve is smaller than T_(alpha, beta)n(1/(1+alpha)), re...
• Penalized maximum likelihood and semiparametric second-order efficiency AI翻译
  作者：Dalalyan, AS; Golubev, GK; Tsybakov, AB
  作者单位：Sorbonne Universite; Aix-Marseille Universite
  摘要：We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asym...
• Extended statistical modeling under symmetry; The link toward quantum mechanics AI翻译
  作者：Helland, Inge S.
  作者单位：University of Oslo
  摘要：We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set A of incompatible experiments, and a transformation group G on the cartesian product Pi of the parameter spaces of these experiments. The set of possible parameters is constrained to lie in a subspace of Pi, an orbit or a set of orbits of G. Each possible model is then connected to a parametric Hilbert space. The spaces of different exp...
• Stable limits of martingale transforms with application to the estimation of Garch parameters AI翻译
  作者：Mikosch, T; Straumann, D
  作者单位：University of Copenhagen; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index alpha is an element of (2, 4). Then, in particular, the marginal distribution of the GARCH process has infinite fourth moment and standard asymptotic theory with normal limits and root n-rates breaks down. This was recently observed by Hall and Yao [Econometrica 71 (2003) 2...
• The shape of incomplete preferences AI翻译
  作者：Nau, Robert
  作者单位：Duke University
  摘要：Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state...
• Efficient parameter estimation for self-similar processes (vol 17, pg 1749, 1989) AI翻译
  作者：Dahlhaus, Rainer
  作者单位：Ruprecht Karls University Heidelberg