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作者：Faria, AE; Smith, JQ
作者单位：University of Warwick
摘要：We address the multivariate version of French's group decision problem where the m members of a group,who are jointly responsible for the decisions they should make, wish to combine their beliefs about the possible Values of n random variables into the group consensus probability distribution. We shall assume the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed partially complete chain graph (PCG) we define in the paper. ...
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作者：Minnotte, MC
作者单位：Utah System of Higher Education; Utah State University
摘要：Given a set of data drawn from an unknown density, it is frequently desirable to estimate the number and location of modes of the density. A test is proposed for the weight of evidence of individual observed modes. The test statistic used is a measure of the size of the mode, the absolute integrated difference between the estimated density and the same density with the mode in question excised at the level of the higher of its two surrounding antimodes. Samples are simulated from a conservativ...
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作者：Devroye, L; Lugosi, G
作者单位：McGill University; Pompeu Fabra University
摘要：We introduce a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L-1 error of the corresponding kernel estimate is not larger than three times the error of the estimate with the optimal smoothing factor plus a constant times root log n/n, where n is the sample size, and the constant depends only on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for each n. The estima...
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作者：Lepski, OV; Spokoiny, VG
作者单位：Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：The problem of optimal adaptive estimation of a function at a given point from noisy data is considered. Two procedures are proved to be asymptotically optimal for different settings. First we study the problem of bandwidth selection for nonparametric pointwise kernel estimation with a given kernel. We propose a bandwidth selection procedure and prove its optimality in the asymptotic sense. Moreover, this optimality is stated not only among kernel estimators with a variable bandwidth. The resu...
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作者：Low, MG
作者单位：University of Pennsylvania
摘要：An inequality is given for the expected length of a confidence interval given that a particular distribution generated the data and assuming that the confidence interval has a given coverage probability over a family of distributions. As a corollary, attempts to adapt to the regularity of the true density within derivative smoothness classes cannot improve the rate of convergence of the length of the confidence interval over minimax fixed-length intervals and still maintain uniform coverage pr...
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作者：Lindsay, BG; Li, B
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The realized error of an estimate is determined not only by the efficiency of the estimator, but also by chance. For example, suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle. Then, intuitively, the longer that vector happens to be, the more accurately its angle is likely to be estimated. Yet this chance, though its information is contained in the data, cannot be accounted for by the variance of the estimate. One way to capture it is by the d...
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作者：Andersson, SA; Madigan, D; Perlman, MD
作者单位：Indiana University System; Indiana University Bloomington; University of Washington; University of Washington Seattle
摘要：Undirected graphs and acyclic digraphs (ADG's), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. Whereas the undirected graph associated with a dependence model is uniquely determine...
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作者：Lindsay, B; Roeder, K
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Carnegie Mellon University
摘要：Consider finite mixture models of the form g(x; Q) = integral f(x; theta)dQ(theta), where f is a parametric density and Q is a discrete probability measure. An important and difficult statistical problem concerns the determination of the number of support points (usually known as components) of Q from a sample of observations from g. For an important class of exponential family models we have the following result: if P has more than p components and Q is an appropriately chosen p-component app...
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作者：Portnoy, S
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Quantile smoothing splines were introduced by Koenker, Ng and Portnoy as natural and appealing estimates of conditional quantiles of response variables. The natural setting for the problem considers minimization of a weighted combination of a fit penalty and a roughness penalty over the space of functions whose derivatives have bounded variation. Although this space is not traditional, Shen has shown recently that the quantile smoothing splines do indeed converge at the usual optimal rate (n(-...
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作者：Gather, U; Hilker, T
作者单位：Dortmund University of Technology
摘要：In 1994 Tyler proposed a modification of the MAD in order to achieve the maximal possible finite sample breakdown point for the Stahel-Donoho estimator based upon the median and the modified MAD. A proof is not given, however, and as far as we know has not been published yet. Moreover there seems to be an error concerning the exact definition of the modified MAD which is needed to achieve this goal. For the sake of theoretical completeness and in order to correct this error we calculate the fi...
