-
作者：Dette, H; Melas, VB; Pepelyshev, A
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrerna of the equi-oscillating best approximation of the function f(0) equivalent to 0 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational, lo...
-
作者：Cai, TT; Low, MG
作者单位：University of Pennsylvania
摘要：A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is developed.
-
作者：Hall, P; Minnotte, MC; Zhang, CM
作者单位：Australian National University; Utah System of Higher Education; Utah State University; University of Wisconsin System; University of Wisconsin Madison
摘要：It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported densities. Our res...
-
作者：Walker, S
作者单位：University of Bath
摘要：We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hettinger and Kullback-Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.
-
作者：Douc, R; Moulines, T; Rydén, T
作者单位：IMT - Institut Mines-Telecom; IMT Atlantique; Lund University
摘要：An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution...
-
作者：Cheng, SW; Ye, KQ
作者单位：Academia Sinica - Taiwan; Montefiore Medical Center; Albert Einstein College of Medicine; Yeshiva University
摘要：Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix could result in different geometric structures, and, thus, different design properties. In this paper...
-
作者：Brown, LD; Carter, AV; Low, MG; Zhang, CH
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick; University of California System; University of California Santa Barbara
摘要：This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields...
-
作者：Mammen, E; Tsybakov, AB
作者单位：University of Mannheim; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
-
作者：Yohai, VJ; Zamar, RH
作者单位：University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of British Columbia
摘要：We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some measures of robustness...
-
作者：Johnstone, IM; Raimondo, M
作者单位：Stanford University; University of Sydney
摘要：We consider the nonparametric estimation of a periodic function that is observed in additive Gaussian white noise after convolution with a boxcar, the indicator function of an interval. This is an idealized model for the problem of recovery of noisy signals and images observed with motion blur. If the length of the boxcar is rational, then certain frequencies are irretreviably lost in the periodic model. We consider the rate of convergence of estimators when the length of the boxcar is irratio...
