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作者：Sun, JY; Loader, C; McCormick, WP
作者单位：University System of Ohio; Case Western Reserve University; AT&T; Alcatel-Lucent; Lucent Technologies; University System of Georgia; University of Georgia
摘要：Generalized linear models (GLM) include many useful models. This paper studies simultaneous confidence regions for the mean response function in these models. The coverage probabilities of these regions are related to tail probabilities of maxima of Gaussian random fields, asymptotically, and hence, the so-called tube formula is applicable without any modification. However, in the generalized linear models, the errors are often nonadditive and non-Gaussian and may be discrete. This poses a cha...
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作者：Buja, A
作者单位：AT&T
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作者：Friedman, J; Hastie, T; Tibshirani, R
作者单位：Stanford University
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作者：Liang, TC
作者单位：Wayne State University
摘要：We exhibit an empirical Bayes test delta(n)(*) for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, delta(n)(*) is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate O(n(-1)(ln n)(1.5)), where n is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is fast...
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作者：Breiman, L
作者单位：University of California System; University of California Berkeley
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作者：Cavalier, L
作者单位：Aix-Marseille Universite
摘要：The aim of tomography is to reconstruct a multidimensional function From observations of its integrals over hyperplanes. We consider the model that corresponds to the case of positron emission tomography. We have n i.i.d. observations from a probability density proportional to Rf, where Rf stands for the Radon transform of the density f. We assume that f is an N-dimensional density such that its Fourier transform is exponentially decreasing. We find an estimator of f which is asymptotically ef...
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作者：Freund, Y; Schapire, RE
作者单位：AT&T
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作者：Chaudhuri, P; Marron, JS
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; University of North Carolina; University of North Carolina Chapel Hill
摘要：Scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation. The family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface. The smoothing parameter here plays the same role as that played by the scale of resolution in a visual system. In this paper, we study in detail various features of that surface from a statistical viewpoint. Pi-Teak convergence of the empirical...
