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作者：DONOHO, DL
作者单位：University of California System; University of California Berkeley
摘要：New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of loss functions. It is also shown that difficulty of estimation is measured by the modulus of continuity ...
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作者：KOUL, HL; OSSIANDER, M
作者单位：Oregon State University
摘要：This paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques. The weights need not be independent, bounded or even square integrable. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in pth-order autoregression models. The latter result, in turn, yields the asymptotic distributions of a class of robust and Jaeckel-type rank estimators. The main result is also us...
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作者：SHAO, PYS; STRAWDERMAN, WE
摘要：The purpose of this paper is to give an explicit estimator dominating the positive-part James-Stein rule. The James-Stein estimator improves on the ''usual'' estimator X of a multivariate normal mean vector theta if the dimension p of the problem is at least 3. It has been known since at least 1964 that the positive-part version of this estimator improves on the James-Stein estimator. Brown's 1971 results imply that the positive-part version is itself inadmissible although this result was assu...
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作者：FLURY, BD
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作者：GOTZE, F; HIPP, C
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：Verifiable conditions are given for the validity of formal Edgeworth expansions for the distribution of sums X(1) + ... + X(n), where X(i) = F(Z(i), ..., Z(i + p - 1)) and Z(1),Z(2), ... is a strict sense stationary sequence that can be written as Z(j) = g(epsilon(j-k): k greater than or equal to 0) with an lid sequence (epsilon(i)) of innovations. These models include nonlinear functions of ARMA processes (Z(i)) as well as certain nonlinear AR processes. The results apply to many statistics i...
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作者：SUN, DC
摘要：Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors in the sense of Ste...
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作者：FINNER, H
摘要：Based on the duality between tests and confidence sets we introduce a new method to derive one-sided confidence bounds following the rejection of a null hypothesis with two-sided alternatives. This method imputes that the experimenter is only interested in confidence bounds if the null hypothesis is rejected. Furthermore, we suppose that he is only interested in the direction and a lower confidence bound concerning the distance of the true parameter value to the parameter values in the null hy...
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作者：BOSE, S
摘要：Uncertainty in specification of the prior distribution is a common concern with Bayesian analysis. The robust Bayesian approach is to work with a class of prior distributions, which model uncertainty about the prior, instead of a single distribution. One is interested in the range of the posterior expectations of certain parametric functions as the prior varies over the class being considered-if this range is small, the analysis is robust to mis-specification of the prior. Relatively little re...
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作者：SHEN, XT; WONG, WH
作者单位：University of Chicago
摘要：In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space and allow the size of...
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作者：GORDON, L; POLLAK, M
作者单位：Hebrew University of Jerusalem
摘要：Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is based on the sequential...
