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作者：Averkamp, R; Houdré, C
作者单位：University of Freiburg; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
摘要：For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median filtering method, lead to asymptotics for denoising heavy tails via wavelet thresholding. Some further comparisons of wavelet thresholding and of kernel estimators are also briefly discussed.
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作者：Hall, P; Kang, KH
作者单位：Australian National University; Hankuk University Foreign Studies
摘要：It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point. where their curvature.,, have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points. then b...
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作者：Leung, DHY
作者单位：Singapore Management University
摘要：A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers ill the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163-184]. However, Under these Circumstances Standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by t...
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作者：Blanchard, G; Geman, D
作者单位：Centre National de la Recherche Scientifique (CNRS); Fraunhofer Gesellschaft; Fraunhofer Germany; Fraunhofer Institute Center Schloss Birlinghoven; Johns Hopkins University
摘要：We explore the theoretical foundations of a twenty questions approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (background) is statistically dominant, and it is imperative to restrict intensive computation...
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作者：Cohen, A; Sackrowitz, HB
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：The problem of multiple endpoint testing for k endpoints is treated as a 2(k) finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), that is, the expected number of acceptances for which the corresponding null hypothesis is false. Th...
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作者：Dalalyan, A
作者单位：Sorbonne Universite
摘要：The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift S(.) is supposed to belong to a nonparametric class of smooth functions of order k >= 1, but the value of k is not known to the statistician. A fully data-driven procedure of estimating the drift function is proposed, using the estimated risk minimization method. The sharp adaptivity of this procedure is proven up to an optimal constant, when the quality of the ...
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作者：Hall, P; Horowitz, JL
作者单位：Australian National University; Northwestern University
摘要：We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the difficulty of which depends on eigenvalues of a ce...
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作者：Wang, XG; Zidek, JV
作者单位：York University - Canada; University of British Columbia
摘要：The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties. However, in order to be effective, the weights involved in its construction need to be judiciously chosen. Choosing those weights is the subject of this article in which we demonstra...
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作者：McCullagh, P
作者单位：University of Chicago
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作者：Xu, HQ; Wu, CFJ
作者单位：University of California System; University of California Los Angeles; University System of Georgia; Georgia Institute of Technology
摘要：A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman-Kempthorne construction of orthogonal arrays, several classes of optimal multi...
