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作者：Hastie, T; Tibshirani, R
作者单位：Stanford University; University of Toronto
摘要：We discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes, and then coupling the estimates together. The coupling model is similar to the Bradley-Terry method for paired comparisons. We study the nature of the class probability estimates that arise, and examine the performance of the procedure in real and simulated data sets. Classifiers used include Linear discriminants, nearest neighbors, adaptive nonlinear methods and the su...
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作者：Chen, SX
作者单位：New York University
摘要：This paper outlines a theoretical framework for finite population models with unequal sample probabilities, along with sampling schemes for drawing random samples from these models. We first present four exact weighted sampling schemes that can be used for any finite population model to satisfy such requirements as ordered/unordered samples, with/without replacement, and fixed/nonfixed sample size. We then introduce a new class of finite population models called weighted polynomial models or, ...
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作者：Peña, EA
作者单位：University System of Ohio; Bowling Green State University
摘要：Consider a counting process (N(t), t epsilon T) with compensator process (A(t), t epsilon T), where A(t) = integral(o)(t)Y(s)lambda(o)(s) ds, (Y(t), t epsilon T) is an observable predictable process, and lambda(0)((.)) is an unknown hazard rate function. A general procedure for extending Neyman's smooth goodness-of-bt test for the composite null hypothesis H-o: lambda(0)((.)) epsilon C = (lambda(0)((.); eta): eta epsilon Gamma subset of or equal to R-q) is proposed and developed. The extension...
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作者：Kim, PT
作者单位：University of Guelph; Yonsei University
摘要：This paper develops nonparametric deconvolution density estimation over SO(N), the group of N x N orthogonal matrices of determinant 1. The methodology is to use the group and manifold structures to adapt the Euclidean deconvolution techniques to this Lie group environment. This is achieved by employing the theory of group representations explicit to SO(N). General consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions. Application t...
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作者：Bose, A
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：We take a unified approach to asymptotic properties of M-m estimates based on i.i.d. observations defined through the minimization of a real-valued criterion function of one or more variables. Our results are applicable to a host of location and scale estimators found in the literature.
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作者：Falk, M
摘要：Given n lid copies X-1,...,X-n of a random element X in some arbitrary measurable space S, we are only interested in those observations that fall into some subset D having but a small probability of occurrence. It is assumed that the distribution P-X of X belongs on D to a parametric family P-X(.boolean AND D) = P-v, V epsilon Theta subset of R-d Nonlinear regression analysis and the peaks-over-threshold (POT) approach in extreme value analysis are prominent examples. For the POT approach on S...
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作者：Drees, H
作者单位：University of Cologne
摘要：Hall and Welsh established the best attainable rate of convergence for estimates of a positive extreme value index gamma under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution. As a first generalization, we obtain a surprisingly sharp bound on the estimation error if gamma is still assumed to be positive, but the rate of convergence of the maximum may be nona...
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作者：Hartigan, JA
作者单位：Yale University
摘要：Consider an estimate theta* of a parameter theta based on repeated observations from a family of densities f(theta) evaluated by the Kullback-Leibler loss function K(theta, theta*) = integral log(f(theta)/f(theta*))f(theta). The maximum likelihood prior density, if it exists, is the density for which the corresponding Bayes estimate is asymptotically negligibly different from the maximum likelihood estimate. The Bayes estimate corresponding to the maximum likelihood prior is identical to maxim...
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作者：Breiman, L
作者单位：University of California System; University of California Berkeley
摘要：Recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error. One of the more effective is bagging. Here, modified training sets are formed by resampling from the original training set, classifiers constructed using these training sets and then combined by voting. Freund and Schapire propose an algorithm the basis of which is to adaptively resample and combine (hence the acronym arcing) so that the weights in the ...
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作者：Donoho, DL; Johnstone, IM
作者单位：Stanford University
摘要：We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets, we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficient. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel- and Besov-type smoothness constraints and asymptotically minimax over Besov bodies with p less than or equal to q. Linear estimates cannot achieve ev...
