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作者：Zuo, YJ; Serfling, R
作者单位：Arizona State University; Arizona State University-Tempe; University of Texas System; University of Texas Dallas
摘要：Statistical depth Functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deep...
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作者：Settimi, R; Smith, JQ
作者单位：University of Chicago; University of Warwick
摘要：We study the geometry of the parameter space for Bayesian directed graphical models with hidden variables that have a tree structure and where all the nodes are binary. We show that the conditional independence statements implicit in such models can be expressed in terms of polynomial relationships among the central moments. This algebraic structure will enable us to identify the inequality constraints on the space of the manifest variables that are induced by the conditional independence assu...
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作者：Kochar, SC; Mukerjee, H; Samaniego, FJ
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; University of California System; University of California Davis; Wichita State University
摘要：In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x, M(x), defined by M(x)= E[X - x\X > z], where X is a lifetime. EA is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (nondecreasing). There is some literature on empirical estimators of M and their properties. Although tests ...
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作者：Almudevar, A; Field, C; Robinson, J
作者单位：Saint Marys University - Canada; Dalhousie University; University of Sydney
摘要：When a unique M-estimate exists, its density is obtained as a corollary to a more general theorem which asserts that under mild conditions the intensity function of the point process of solutions of the estimating equations exists and is given by the density of the estimating function standardized by multiplying it by the inverse of its derivative. We apply the results to give a result for Huber's proposal 2 applied to regression and scale estimates. We also give a saddlepoint approximation fo...
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作者：Janssen, A
作者单位：Heinrich Heine University Dusseldorf
摘要：It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away from the corresponding Neyman-Pearson test level points except for a finite number of orthogonal direct...
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作者：Dress, H; de Haan, L; Resnick, S
作者单位：University of Cologne; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Cornell University
摘要：An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Will estimator is a popular method for doing this but its practical use is encumbered by several difficulties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method unless the underlying data comes from a Pareto distribution.
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作者：Beibel, M
作者单位：University of Freiburg
摘要：We study the continuous time analogue of the Bayes problem of Poor. As usual the results on the optimal solution are more explicit than in the discrete time set-up.
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作者：Breidt, FJ; Opsomer, JD
作者单位：Colorado State University System; Colorado State University Fort Collins; Iowa State University; Iowa State University
摘要：Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are considerably weaker. The estimators are shown to be asymptotically design-unbiased and consistent under mil...
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作者：Shapiro, A
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and, more generally, M-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set S. We give a counterexample showing that regularity of S in the sense of Clarke is not; sufficient for asymptotic equivalence of rootn-consistent locally optimal M-estimators. We argue further that stronger properties, such as so-called near convexity or prox-regularit...
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作者：Friedman, J; Hastie, T; Tibshirani, R
作者单位：Stanford University; Stanford University; United States Department of Energy (DOE); SLAC National Accelerator Laboratory; Stanford University
摘要：Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted Versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of well-known statistical pr...
