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作者：Donoho, DL
作者单位：Stanford University
摘要：We study a simple horizon model for the problem of recovering an image from noisy data; in this model the image has an edge with alpha-Holder regularity. Adopting the viewpoint of computational harmonic analysis, we develop an overcomplete collection of atoms called wedgelets, dyadically organized indicator functions with a variety of locations, scales and orientations. The wedgelet representation provides nearly optimal representations of objects in the horizon model, as measured by minimax d...
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作者：Eggermont, PPB; LaRiccia, VN
作者单位：University of Delaware
摘要：We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to L(1) convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.
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作者：Jiang, WX; Tanner, MA
作者单位：Northwestern University
摘要：We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(alpha + x(T)beta) are mixed. Here psi(.) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(x)) where h(.) is an element of W-2; K0(infinity) (a Sobolev class over [0, 1](s)). It is shown that the HME probabili...
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作者：Walker, S; Muliere, P
作者单位：Imperial College London; University of Pavia
摘要：In this paper we present a new characterization and perspective on a neutral to the right prior. This characterization is based on a sequence of predictive laws which provides explicitly the posterior parameters and Bayes estimators for such a prior.
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作者：Koul, HL; Stute, W
作者单位：Michigan State University; Justus Liebig University Giessen
摘要：This paper studies a class of tests useful for testing the goodness-of-fit of an autoregressive model. These tests are based on a class of empirical processes marked by certain residuals. The paper first gives their large sample behavior under null hypotheses. Then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free. Consistency of these tests is also discussed briefly.
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作者：Van Keilegom, I; Akritas, MG
作者单位：Maastricht University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Consider a heteroscedastic regression model Y = m(X) + sigma(X)epsilon, where the functions m and sigma are smooth, and epsilon is independent of X. The response variable Y is subject to random censoring, but it is assumed that there exists a region of the covariate X where the censoring of Y is light. Under this condition, it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring. Crucial ...
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作者：Chen, KN; Hu, IC; Ying, ZL
作者单位：Hong Kong University of Science & Technology; Hong Kong University of Science & Technology; Rutgers University System; Rutgers University New Brunswick
摘要：Strong consistency for maximum quasi-likelihood estimators of regression parameters in generalized Linear regression models is studied. Results parallel to the elegant work of Lai, Robbins and Wei and Lai and Wei on least squares estimation under both fixed and adaptive designs are obtained. Let y(1),..., y(n) and x(1),...,x(n) be the observed responses and their corresponding design points (p x 1 vectors), respectively. For fixed designs, it is shown that if the minimum eigenvalue of Sigma x(...
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作者：Del Barrio, E; Cuesta-Albertos, JA; Matrán, C; Rodríguez-Rodríguez, JM
作者单位：Universidad de Valladolid; Universidad de Cantabria
摘要：Ne consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance me obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of the statistic is studied using approximations of the quantile process by Brownian bridges. This method differs from the ad hoc method of de Wet and Venter and permits a similar analysis for testing other location scale famil...
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作者：Mammen, E; Tsybakov, AB
作者单位：Ruprecht Karls University Heidelberg; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Discriminant analysis for two data sets in R-d with probability densities f and g can be based on the estimation of the set G = {x:f(x) greater than or equal to g(x)}. We consider applications where it is appropriate to assume that the region G has a smooth boundary or belongs to another nonparametric class of sets. In particular, this assumption makes sense if discrimination is used as a data analytic tool. Decision rules based on minimization of empirical risk over the whole class of sets an...
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作者：Pensky, M; Vidakovic, B
作者单位：State University System of Florida; University of Central Florida; Duke University
摘要：The problem of estimating a density g based on a sample X-1, X-2, X-n from p = q * g is considered. Linear and nonlinear wavelet estimators teased on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space H-alpha. Moreover, the estimators considered in this paper adjust automatically to the situation when g is supersmooth.
