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作者：Aslan, Mihaela
作者单位：US Department of Veterans Affairs; Veterans Health Administration (VHA); VA Connecticut Healthcare System; Yale University
摘要：Given a random sample from a distribution with density function that depends on an unknown parameter 0, we are interested in accurately estimating the true parametric density function at a future observation from the same distribution. The asymptotic risk of Bayes predictive density estimates with Kullback-Leibler loss function D(f(theta)parallel to(f) over cap) = integral (f) over cap (theta) log (f(theta)/(f) over cap) is used to examine various ways of choosing prior distributions; the prin...
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作者：Cai, T. Tony; Low, Mark G.
作者单位：University of Pennsylvania
摘要：Adaptive estimation of a quadratic functional over both Besov and L(p) balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and L(p) balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and L(p) balls in the sense that it attains certain constra...
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作者：Carroll, Raymond J.; Ruppert, David
作者单位：Texas A&M University System; Texas A&M University College Station; Cornell University
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作者：Fromont, Magalie; Laurent, Beatrice
作者单位：Universite Rennes 2; Universite de Rennes; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
摘要：Given an i.i.d. sample drawn from a density f, we propose to test that f equals some prescribed density fo or that f belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the L-2-distance between f and fo or between f and the parametric family that we consider. For each sample size n, our test has level of significance a. In the case of simple hypotheses, we prove that our test is adaptive: it achieves the optimal rates of testing establi...
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作者：Mei, YJ
作者单位：Fred Hutchinson Cancer Center; California Institute of Technology
摘要：In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution f(theta) and tries to minimize the detection delay for every possible post-change distribution g(lambda). In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every poss...
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作者：Scricciolo, Catia
作者单位：Bocconi University
摘要：We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p, The posterior expected density provides a nonparametric estimation procedure attaining the optimal minimax rate of convergence under Hellinger loss if the posterior distribution achieves the optimal rate over certain uniformity classes. A prior on the density class of interest is induced by a prior on the coefficient...
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作者：Hall, Peter; Vial, Celine
作者单位：Australian National University; Universite Paris Nanterre
摘要：The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore statistical proper...
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作者：Robinson, Peter M.; Zaffaroni, Paolo
作者单位：University of London; London School Economics & Political Science; Imperial College London
摘要：Strong consistency and asymptotic normality of the Gaussian pseudomaximum likelihood estimate of the parameters in a wide class of ARCH(infinity) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.
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作者：Zhu, Hongtu; Zhang, Heping
作者单位：Columbia University; New York State Psychiatry Institute; Yale University; Jiangxi Normal University
摘要：Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the existing testing procedures depend on restrictive assumptions. In this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero. Under some mild condition...
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作者：Marinucci, Domenico
作者单位：University of Rome Tor Vergata
摘要：In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the sample size grows. The results we present are then exploited in a set of procedures aimed at testing non-Gaussianity; for these statistics, we are able to show convergence to functionals of standard Brownian motion under the null hypothesis. Analytic results are...
