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作者：BOSE, A; BOUKAI, B
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：We consider the problem of sequentially estimating one parameter in a class of two-parameter exponential family of distributions. We assume a weighted squared error loss with a fixed cost of estimation error. The stopping rule, based on the maximum likelihood estimate of the nuisance parameter, is shown to be independent of the terminal estimate. The asymptotic normality of the stopping variable is established and approximations to its mean and to the regret associated with it are also provide...
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作者：SIEGMUND, D; ZHANG, HP
作者单位：Yale University
摘要：Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.
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作者：CRITCHLEY, F; MARRIOTT, P; SALMON, M
作者单位：University of Surrey; European University Institute
摘要：A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g., any point theta may be the true parameter) and preferred point ones (e.g., when theta0 is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its relationship to statistical manifolds, in particular to Amari...
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作者：SEIDENFELD, T; WASSERMAN, L
摘要：Suppose that a probability measure P is known to lie in a set of probability measures M. Upper and lower bounds on the probability of any event may then be computed. Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds on the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred. In addition to being an interesting statistical curiosity, this counterintui...
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作者：DAVIES, PL
摘要：Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that S-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of ...
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作者：GASSIAT, E
摘要：We consider the estimation problem of the parameter b of a stationary AR(p) process without any of the usual causality assumptions. The aim of the paper is to derive asymptotic minimax bounds for estimators of b. When the distribution of the noise is known, we show LAN properties of the model and derive locally asymptotically minimax (LAM) estimators. The most important results are about the case of unknown distribution: The main result shows that, if one uses the usual parametrization, these ...
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作者：DAWID, AP; LAURITZEN, SL
作者单位：Aalborg University
摘要：This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov probabilities, using a...
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作者：THOMPSON, GL
摘要：Exploratory graphical methods for fully and partially ranked data are proposed. In fully ranked data, n items are ranked in order of preference by a group of judges. In partially ranked data, the judges do not completely specify their ranking of the n items. The resulting set of frequencies is a function on the symmetric group of permutations if the data is fully ranked, and a function on a coset space of the symmetric group if the data is partially ranked. Because neither the symmetric group ...
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作者：BARRY, D
摘要：Observations y(ij) are made at points (x1i, x2j) according to the model y(ij) = F(x1i, x2j) + e(ij), where the e(ij) are independent normals with constant variance. In order to test that F(x1, x2) is an additive function of x1 and x2, a likelihood ratio test is constructed comparing F(x1, X2) = mu + Z1(x1) + Z2(x2) with F(x1, x2) = mu + Z1(x1) + Z2(x2) + Z(x1, x2), where Z1, Z2 are Brownian motions and Z is a Brownian sheet. The ratio of Brownian sheet variance to error variance alpha is chose...
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作者：LELE, C
摘要：In this paper we consider the problem of estimating the loss of point estimators and study admissibility of such estimators of loss. We adapt and extend the ''unified admissibility proof'' idea of Brown and Hwang to this problem. We first present the result in the Gaussian setup. We then generaIize the procedure to general exponential family distributions and apply it to the Poisson distribution. The result for the gamma distribution is also stated. The role played by the ''polydisc transform'...
