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作者：Desolneux, A; Moisan, L; Morel, JM
作者单位：Universite Paris Saclay
摘要：We discuss the mathematical properties of a recently introduced method for computing geometric structures in a digital image without any a priori information. This method is based on a basic principle of perception which we call the Helmholtz principle. According to this principle, an observed geometric structure is perceptually meaningful if the expectation of its number of occurrences (in other words, its number of false alarms, NF) is very small in a random image. It is maximal meaningful i...
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作者：Tripathi, G; Kitamura, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania
摘要：Let (x,z) be a pair of observable random vectors. We construct a new smoothed empirical likelihood-based test for the hypothesis E{g(z, theta) \x} = 0 w.p. 1, where g is a vector of known functions and theta an unknown finite-dimensional parameter. We show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives. Furthermore, the test is shown to possess an optimality property in large samples. Simu...
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作者：Shafie, K; Sigal, B; Siegmund, D; Worsley, KJ
作者单位：Shahid Beheshti University; Stanford University; Stanford University; McGill University
摘要：Siegmund and Worsley considered the problem of testing for a signal with unknown location and scale in a Gaussian random field defined on RN. The test statistic was the maximum of a Gaussian random field in an (N + 1)-dimensional scale space, N dimensions for location and one dimension for the scale of a smoothing kernel. Siegmund and Worsley used two methods, one involving the expected Euler characteristic of the excursion set and the other involving the volume of tubes, to derive an approxim...
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作者：Reid, N
作者单位：University of Toronto
摘要：Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years provides an illustration of the interplay between techniques of approximation and statistical theory.
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作者：Marcheselli, M
作者单位：University of Siena
摘要：The asymptotic behavior of jackknife estimators and jackknife variance estimators is investigated for nonsmooth functions of the sample mean vector. An application of jackknifing a suitable estimator of the intrinsic diversity profile is also presented.
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作者：Clerc, M; Mallat, S
作者单位：Universite Cote d'Azur; Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Institut Polytechnique de Paris; Ecole Polytechnique; New York University
摘要：This paper studies classes of nonstationary processes, such as warped processes and frequency-modulated processes, that result from the deformation of stationary processes. Estimating deformations can often provide important information about an underlying physical phenomenon. A computational harmonic analysis viewpoint shows that the deformed autocovariance satisfies a transport equation at small scales, with a velocity proportional to a deformation gradient. We derive an estimator of the def...
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作者：Claeskens, G; Van Keilegom, I
作者单位：Texas A&M University System; Texas A&M University College Station; Universite Catholique Louvain
摘要：Confidence bands for regression curves and their first p derivatives are obtained via local pth order polynomial estimation. The method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations. As an alternative to the confidence bands obtained by asymptotic distribution theory, we also study smoothed bootstrap confidence bands. Simulations illustrate the finite sample properties of the methodology.
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作者：Groeneboom, P; Lopuhaä, HP; De Wolf, PP
作者单位：Delft University of Technology
摘要：A large part of the theory of extreme value index estimation is developed for positive extreme value indices. The best-known estimator of a positive extreme value index is probably the Hill estimator. This estimator belongs to the category of moment estimators, but can also be interpreted as a quasi-maximum likelihood estimator. It has been generalized to a kernel-type estimator, but this kernel-type estimator can, similarly to the Hill estimator, only be used for the estimation of positive ex...
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作者：Ducharme, GR; Ledwina, T
作者单位：Universite de Montpellier; Polish Academy of Sciences
摘要：The notion of efficient test for a Euclidean parameter in a semiparametric model was introduced by Stein [Proc. Third Berkeley Symp. Math. Statist. Probab. 1 (1956) 187-195]. Such tests are locally most powerful for a wide class of infinite-dimensional nuisance parameters. The first formal application of this notion to a suitably parametrized two-sample problem was provided by Hajek [Ann. Math. Statist. 33 (1962) 1124-1147]. However, this and subsequent solutions appear to be not well-suited f...
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作者：Storey, JD
作者单位：University of Washington; University of Washington Seattle
摘要：Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all significant hypotheses. The FDR is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests. In this work, we introduce a mod...
