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作者：Jones, LK
作者单位：University of Massachusetts System; University of Massachusetts Lowell
摘要：A criterion for local estimation and approximation in nonlinear regression and neural network training is introduced and motivated. Nth-order greedy approximation for the regression (or target) function based on the criterion is shown to converge at rate O(1/N-1/2) in the nonsampling case.
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作者：Li, L; Speed, TP
作者单位：State University System of Florida; Florida State University; University of California System; University of California Berkeley
摘要：This paper describes a parametric deconvolution method (PDPS) appropriate for a particular class of signals which we call spike-convolution models. These models arise when a sparse spike train-Dirac deltas according to our mathematical treatment-is convolved with a fixed point-spread function, and additive noise or measurement error is superimposed. We view deconvolution as an estimation problem, regarding the locations and heights of the underlying spikes, as well as the baseline and the meas...
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作者：Ghosal, S; Sen, A; van der Vaart, W
作者单位：Vrije Universiteit Amsterdam; University of Hyderabad
摘要：We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.
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作者：Draper, NR; Heiligers, B; Pukelsheim, F
作者单位：University of Wisconsin System; University of Wisconsin Madison; Otto von Guericke University; University of Augsburg
摘要：For mixture models an the simplex, we discuss the improvement of a given design in terms of increasing symmetry, as well as obtaining a larger moment matrix under the Loewner ordering. The two criteria together define the Kiefer design ordering. For the second-degree mixture model, we show that the set of weighted centroid designs constitutes a convex complete class for the Kiefer ordering. For four ingredients, the class is minimal complete. Of essential importance for the derivation is a cer...
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作者：Zhao, LH
作者单位：University of Pennsylvania
摘要：We study the Bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation. We consider the asymptotic properties of Bayes procedures for conjugate (=Gaussian) priors. We show that so long as the prior puts nonzero measure on the very large parameter sat of interest then the Bayes estimators are not satisfactory. More specifically, we show that these estimators do not achieve the correct minim:ur rate over norm bounded sets in the parame...
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作者：Inglot, T; Kallenberg, WCM; Ledwina, T
作者单位：University of Wroclaw; University of Twente; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
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作者：Kunert, J; Martin, RJ
作者单位：Dortmund University of Technology; University of Sheffield
摘要：This paper generalizes Kushner's method for finding optimal repeated measurements designs to find optimal designs under an interference model. The model we assume is for a one-dimensional layout without guard plots and with different left and right neighbor effects. The resulting optimal designs may need many blocks or may not even exist as a finite design. The results give lower bounds for optimality criteria on finite designs and the design structure can be used to suggest efficient small de...
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作者：Pronzato, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：We consider the situation where one has to maximize a function eta(theta, x) with respect to x is an element of R-q, when a is unknown and estimated by least squares through observations y(k) = f(inverted perpendicular)(x(k))theta + epsilon (k), with epsilon (k) some random error. Classical applications are regulation and extremum control problems. The approach we adopt corresponds to maximizing the sum of the current estimated objective and a penalization for poor estimation: x(k+1) maximizes...
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作者：Juditsky, A; Nemirovski, A
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Technion Israel Institute of Technology
摘要：We consider the problem of estimating an unknown function f from N noisy observations on a random grid. In this paper we address the following aggregation problem: given M functions f(1),...,f(M) find an aggregated estimator which approximates f nearly as well as the best convex combination f* of f(1),...,f(M). We propose algorithms which provide approximations of f* with expected L-2 accuracy O(N(-1/)4 ln(1/4) M). We show that this approximation rate cannot be significantly improved. We discu...
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作者：Morgan, JP; Bailey, RA
作者单位：Old Dominion University; University of London; Queen Mary University London
摘要：Designs for sets of experimental units with many blocking factors are studied. It is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form. In consequence, a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest, in a sense which is made precise in the paper. This encompasses several previous results for optimal designs with more than one bl...
