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• Spatial extremes: Models for the stationary case AI翻译
  作者：De Haan, L; Pereira, TT
  作者单位：Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC; Universidade de Lisboa
  摘要：The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and Pickands [Probab. Theory Related Fields 72 (1986) 477-492]. We propose three one-dimensional and three two-dimensional models. These models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the di...
• Local partial-likelihood estimation for lifetime data AI翻译
  作者：Fan, Jianqing; Lin, Huazhen; Zhou, Yong
  作者单位：Chinese University of Hong Kong; Princeton University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Sichuan University
  摘要：This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a one-step local partial-likel...
• 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...
• Serial and nonserial sign-and-rank statistics: Asymptotic representation and asymptotic normality AI翻译
  作者：Hallin, M; Vermandele, C; Werker, B
  作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Tilburg University; Universite Libre de Bruxelles; Universite Libre de Bruxelles
  摘要：The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the absence of a symmetry assumption, is considered as a location parameter, the maximal invariance property of ordinary ranks is lost to the ranks and the signs. This new maximal invariant thus suggests a new class of statistics, based on ordinary ranks and sig...
• Asymptotic normality of extreme value estimators on C[0,1] AI翻译
  作者：Einmahl, John H. J.; Lin, Tao
  作者单位：Tilburg University; Xiamen University
  摘要：Consider n i.i.d. random elements on C[0, 1]. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution. A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0, 1]. Detailed examples are also presented.
• False discovery and false nondiscovery rates in single-step multiple testing procedures AI翻译
  作者：Sarkar, Sanat K.
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
  摘要：Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explai...
• Optimal change-point estimation from indirect observations AI翻译
  作者：Goldenshluger, A.; Tsybakov, A.; Zeevi, A.
  作者单位：University of Haifa; Columbia University; Sorbonne Universite; Universite Paris Cite
  摘要：We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degre...