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作者：DONNELL, DJ; BUJA, A; STUETZLE, W
作者单位：Telcordia Technologies
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作者：LAI, TL
摘要：Stochastic regression models of the form y(i) = f(i)(theta) + epsilon(i), where the random disturbances epsilon(i) form a martingale difference sequence with respect to an increasing sequence of sigma-fields {g(i)} and f(i) is a random g(i-1)-measurable function of an unknown parameter theta, cover a broad range of nonlinear (and linear) time series and stochastic process models. Herein strong consistency and asymptotic normality of the least squares estimate of theta in these stochastic regre...
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作者：TIERNEY, L
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作者：FAN, JQ; HALL, P
作者单位：Australian National University
摘要：The local median regression method has long been known as a robustified alternative to methods such as local mean regression. Yet, its optimal statistical properties are largely unknown. In this paper, we show via decision-theoretic arguments that a local weighted median estimator is the best least absolute deviation estimator in an asymptotic minimax sense, under L(1)-loss. We also study asymptotic efficiency of the local median estimator in the class of all possible estimators. From a practi...
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作者：MASSAM, H
摘要：A class of exponential transformation models is defined on symmetric cones OMEGA with the group of automorphisms on OMEGA as the acting group. We show that these models are reproductive and the exponent of their joint distribution for a given sample of size q can be split into q independent components, introducing one sample point at a time. The automorphism group can be factorized into the group of positive dilation and another group. Accordingly, the symmetric cone OMEGA can be seen as the d...
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作者：STONE, CJ
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作者：BESAG, J
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作者：CHANG, IS; HSIUNG, CA
作者单位：Academia Sinica - Taiwan
摘要：This paper indicates that a minor modification of the maximum likelihood estimate of Vardi, Shepp and Kaufman can be regarded as a step in the standard nonparametric MLE by the method of sieves and establishes the asymptotic consistency for it. This method of sieves suggests that the number of pixels needs to be in line with the number of detectors in order to avoid poor image reconstructions. a simulation study is also presented to support this suggestion.
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作者：HARTIGAN, JA
摘要：Observations X(i) are uncorrelated with means theta(i), i = 1,...,n, and variances 1. The linear estimators theta = TX, for some n x n matrix T, are widely used in smoothing problems, where it is assumed that neighbouring parameter Values are similar The smoothness assumption is violated in change point problems, where neighbouring parameter values are equal, except at some unspecified change points where there are jumps of unknown size from one parameter value to the next. In the case of a si...
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作者：TAKAGI, Y
摘要：Hajek established a local asymptotic minimax risk bound for appropriate symmetric loss functions and also gave a necessary condition for the risk of an estimator to attain the lower bound. We extend these results to the case of asymmetric loss functions. The asymmetry brings about the shift of location of the loss functions. Besides, the optimal estimator that attains the bound is shown to have asymptotic normal distribution with asymptotic bias.
