-
作者：Genovese, Christopher; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f* which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f* and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.
-
作者：Wang, Lie; Brown, Lawrence D.; Cai, T. Tony; Levine, Michael
作者单位：University of Pennsylvania; Purdue University System; Purdue University
摘要：Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results indicate that, contrary to the common practice, it is not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean when the mean function is not smooth. Instead it is more desirable to use estimators of ...
-
作者：Anderes, Ethan B.; Stein, Michael L.
作者单位：University of California System; University of California Berkeley; University of Chicago
摘要：This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on R-2 based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package-from model assumptions to algorithmic recovery of the deformation-for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.
-
作者：Chambaz, Antoine; Rousseau, Judith
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors are shown to be O(e(-an)) and O((log n)(b) / root n) (a, b > 0), respectively.
-
作者：Zhang, Zhengjun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher's Z-transformation test may fail to reach a right conclusion. Unlike most asymptotic te...
-
作者：Moustakides, George V.
作者单位：University of Patras
摘要：In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better understanding most well-known criteria and also propose new ones. For a specific new criterion that constitutes an extension to Lorden's performance measure, we offer the optimum structure for detecting a change in the constant drift of a Brownian motion and a for...
-
作者：von Luxburg, Ulrike; Belkin, Mikhail; Bousquet, Olivier
作者单位：Max Planck Society; University System of Ohio; Ohio State University
摘要：Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new methods to establish that, for increasing sample size, those eigenvectors converge to the eigenvectors of...
-
作者：Hobert, James P.; Marchev, Dobrin
作者单位：State University System of Florida; University of Florida; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; Baruch College (CUNY)
摘要：The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo (MCMC) algorithm that is based on a Markov transition density of the form p(x vertical bar x') = integral y fx vertical bar y (x vertical bar y)fY vertical bar X (y vertical bar x') dy, where fX vertical bar Y and fY vertical bar X are conditional densities. The PX-DA and marginal augmentation algorithms of Liu and Wu [J. Amer. Statist. Assoc. 94 (1999) 1264-1274] and Meng and van Dyk [Biometrika 86 (1999) 301-320] ...
-
作者：van de Geer, Sara A.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.
