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作者：Fuh, CD
作者单位：Academia Sinica - Taiwan
摘要：Let xi(0),xi(1),...,xi(omega-1) be observations from the hidden Markov model with probability distribution P(theta)0, and let xi(omega), xi(omega+1),... be observations from the hidden Markov model with probability distribution P(theta)1. The parameters theta(0) and theta(1) are given, while the change point omega is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from P(theta)0 to P(theta)1, but to avoid false alarms. Specifically, we seek a stoppi...
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作者：Huang, TM
作者单位：Iowa State University
摘要：The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.
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作者：Donoho, D; Jin, JS
作者单位：Stanford University
摘要：Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested comparing the fraction of observed significances at a given alpha-level to the expected fraction under the joint null. In fact, he suggested standardizing the difference of the two quantities and forming a z-score; the r...
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作者：Johnstone, IM; Silverman, BW
作者单位：Stanford University; University of Oxford
摘要：An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density gamma, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If estimation is then carried Out using the posterior median, this is a random thresholding procedure. Other thresholding rules employing...
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作者：Peng, L
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the domain of attraction of a stable law with index between 1 and 2. In this article we use a method similar to Qin and Wong [Scand. J. Statist. 23 (1996) 209-219] to derive an empirical-likeillood-based confidence interval for the mean when the underlying distribut...
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作者：Schick, A; Wefelmeyer, W
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; University of Cologne
摘要：Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary distribution of the process. The usual estimator would be the empirical estimator. It can be improved using the fact that the innovations are centered. We construct an even better estimator using the representation of the observations as infinite-order moving averag...
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作者：Koltchinskii, V
作者单位：University of New Mexico
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作者：Zuo, YJ; Cui, HJ; He, XM
作者单位：Michigan State University; University of Illinois System; University of Illinois Urbana-Champaign; Beijing Normal University
摘要：The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a desirable balance betw...
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作者：Hall, P; Ooi, H
作者单位：Australian National University
摘要：We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue that the simplest form of that method suffers from the same difficulties that inhibit level accuracy of Silverman's bandwidth-based test for modality: the conditional distribution of the bootstrap form of a density estimator is not a good approximation to the ...
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作者：Chan, G; Wood, ATA
作者单位：University of Iowa; University of Nottingham
摘要：We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g {X (t)}, where g: R --> R is an unknown smooth function and X (t) is a real-valued stationary Gaussian field on R-d d = 1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is fixed domain (or infill) asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat richer than in t...
