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作者：Stufken, John; Tang, Boxin
作者单位：University System of Georgia; University of Georgia; Simon Fraser University
摘要：Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = lambda 2(d). Our results not only give the number of nonisomorphic orthogonal arrays for given d...
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作者：Audibert, Jean-Yves; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Sorbonne Universite
摘要：It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n(-1/2). The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n(-1), and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are not correct. In...
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作者：Lahiri, P.; Mukherjee, Kanchan
作者单位：University System of Maryland; University of Maryland College Park; University of Liverpool
摘要：We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of uncertainty of our proposed e...
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作者：Steinwart, Ingo; Scovel, Clint
作者单位：United States Department of Energy (DOE); Los Alamos National Laboratory
摘要：For binary classification we establish learning rates up to the order of n(-1) for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometric noise condition which is used to bound the approximation error. Unlike previously proposed concepts for bounding the approximation error, the geometric noise assumption does not ...
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作者：Braess, Dietrich; Dette, Holger
作者单位：Ruhr University Bochum
摘要：We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior for these parameters is available. On interval parameter spaces, it was observed empirically by many authors that an increase of uncertainty in the prior information (i.e., a larger range for the parameter space in the maximin criterion or a larger ...
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作者：Andrews, Beth; Davis, Richard A.; Breidt, F. Jay
作者单位：Northwestern University; Colorado State University System; Colorado State University Fort Collins
摘要：An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based resid...
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作者：Ghosal, Subhashis; van der Vaart, Aad
作者单位：North Carolina State University; Vrije Universiteit Amsterdam
摘要：We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth is given a sequence of priors which is obtained by scaling a single prior by an appropriate order. In order to handle this problem, we derive a new general rate theorem by considering a countable covering of the parameter space whose prior probabilities sat...
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作者：Banerjee, Moulinath; Mckeague, Ian W.
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We investigate the problem of finding confidence sets for split points in decision trees (CART). Our main results establish the asymptotic distribution of the least squares estimators and some associated residual sum of squares statistics in a binary decision tree approximation to a smooth regression curve. Cube-root asymptotics with nonnormal limit distributions are involved. We study various confidence sets for the split point, one calibrated using the subsampling bootstrap, and others calib...
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作者：Butucea, Cristina; Guta, Madalin; Artiles, Luis
作者单位：Universite Paris Nanterre; Utrecht University
摘要：We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum Systems. The state is represented through the Wigner function, a generalized probability density on R-2 which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The effect of the losses due to detection inefficiencies, which are always present in a real experiment, is the addition to the tomographic data of ind...
