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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...
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作者：Liu, W
作者单位：University of Southampton
摘要：A new sequential sampling scheme is proposed in which, after an initial batch sample, sampling is continued in batches of data-dependent sizes (at most k such batches), and then one-at-a-time with a data-dependent stopping rule. This new scheme requires about the same sample size as the fully sequential Anscombe-Chow-Robbins (ACR) sampling scheme but substantially fewer sampling operations. The problem of constructing fixed-width confidence intervals for the mean of a normal population with un...
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作者：Robinson, PM
作者单位：University of London; London School Economics & Political Science
摘要：A central limit theorem is given for certain weighted partial sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel nonparametric fixed-design regression, giving a single central limit theorem which indicates how error spectral behavior at only zero frequency influences the asymptotic distribution and covers long-range, short-range and negative dependence. We show how the regression e...
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作者：Walther, G
作者单位：Stanford University
摘要：The Kolmogorov-Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate settings, an analogous role is played by the halfspace distance, which has the merit of being invariant under linear transformations. However, the evaluation of the halfspace distance between two samples is a computationally very intensive combinatorial problem even in moderate dimensions, which severely restricts the use of the halfspace distance, especially ...
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作者：Yakir, B
作者单位：Hebrew University of Jerusalem
摘要：Suppose X-1, X-2,..., Xv-1 are lid random variables with distribution F-0, and X-v, Xv+1,... are are lid with distributed F-1. The change point v is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from F-0 to F-1 (detect the change), but to avoid false alarms. Pollak found a version of the Shiryayev-Roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a...
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作者：Zhao, LC; Bai, ZD; Chao, CC; Liang, WQ
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; National Sun Yat Sen University; Academia Sinica - Taiwan
摘要：An error bound in the normal approximation to the distribution of the double-indexed permutation statistics is derived. The derivation is based on Stein's method and on an extension of a combinatorial method of Bolthausen. The result can be applied to obtain the convergence rate of order n(-1/2) for some rank-related statistics, such as Kendall's tau, Spearman's rho and the Mann-Whitney-Wilcoxon statistic. Its applications to graph-related nonparametric statistics of multivariate observations ...
