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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...
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作者：Phillips, PCB; Shimotsu, K
作者单位：Yale University; Queens University - Canada
摘要：Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d less than or equal to 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a polynomial trend of order alpha > 1/2, the estimator is shown to be inconsistent and to converge in probability to unity.
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作者：Hallin, M; Lu, ZD; Tran, LT
作者单位：Universite Libre de Bruxelles; Chinese Academy of Sciences; University of London; London School Economics & Political Science; Indiana University System; Indiana University Bloomington
摘要：A local linear kernel estimator of the regression function x --> g(x) := E[Y-i\X-i = x], X is an element of R-d, of a stationary (d + 1)-dimensional spatial process {(Y-i, X-i), i is an element of Z(N)} observed over a rectangular domain of the form l(n) := {i = (i(1),..., i(N)) is an element of Z(N)\ 1 less than or equal to i(k) less than or equal to n(k), k = 1,..., N}, n = (n(1),..., n(N)) is an element of Z(N), is proposed and investigated. Under mild regularity assumptions, asymptotic nor...
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作者：Nieto-Barajas, LE; Prünster, I; Walker, SG
作者单位：University of Pavia; University of Kent
摘要：This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we present results for the distribution of means under both prior and posterior conditions and, via the use of strategic latent variables, undertake a full Bayesian analysis. Our class of priors includes the well-known and widely used mixture of a Dirichlet proce...
