The Annals of Statistics

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• Local extremes, runs, strings and multiresolution AI翻译
  作者：Davies, PL; Kovac, A
  作者单位：University of Duisburg Essen
  摘要：The paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes. Two methods, the run method and the taut-string multiresolution method, are introduced and analyzed on standard test beds. It is shown that the number and locations of local extreme values are consistently estimated. Rates of convergence are proved for both methods. The run method converges slowly but can withstand blocks as well as a high proportion of isolated outliers. The ...
• Regularity and uniqueness for constrained M-estimates and redescending M-estimates AI翻译
  作者：Kent, JT; Tyler, DE
  作者单位：University of Leeds; Rutgers University System; Rutgers University New Brunswick
  摘要：Constrained M-estimates of multivariate location and scatter are found by finding the global minimum of an objective function subject to a constraint. They are related to redescending M-estimates of multivariate location and scatter since any stationary point of the objective function corresponds to such an M-estimate. Unfortunately, even for the population form of the estimator, that is, the constrained dl-functional, the objective function may have multiple stationary points. In this paper, ...
• Nonparametric analysis of covariance AI翻译
  作者：Dette, H; Neumeyer, N
  作者单位：Ruhr University Bochum
  摘要：In the problem of testing the equality of k regression curves from independent samples, we discuss three methods using nonparametric estimators of the regression function. The first test is based on a linear combination of estimators for the integrated variance function in the individual samples and in the combined sample. The second approach transfers the classical one-way analysis of variance to the situation of comparing nonparametric curves, while the third test compares the differences be...
• Local greedy approximation for nonlinear regression and neural network training AI翻译
  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.
• Parametric deconvolution of positive spike trains AI翻译
  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...
• Testing monotonicity of regression AI翻译
  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.
• Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients AI翻译
  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...
• Bayesian aspects of some nonparametric problems AI翻译
  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...
• Vanishing shortcoming and asymptotic relative efficiency (vol 28, pg 215, 2000) AI翻译
  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
• On the determination of optimal designs for an interference model AI翻译
  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...