2011

最新文章

• DELTA METHOD IN LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR ESTIMATORS AI翻译
  作者：Gao, Fuqing; Zhao, Xingqiu
  作者单位：Wuhan University; Hong Kong Polytechnic University; Zhongnan University of Economics & Law
  摘要：The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large deviations is proposed. The new method can be widely applied to driving the moderate deviations of estima...
• ASYMPTOTIC EQUIVALENCE FOR INFERENCE ON THE VOLATILITY FROM NOISY OBSERVATIONS AI翻译
  作者：Reiss, Markus
  作者单位：Humboldt University of Berlin
  摘要：We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function a and a nonstandard noise level. As an application, new rate-optimal estimators of the v...
• RATES OF CONVERGENCE IN ACTIVE LEARNING AI翻译
  作者：Hanneke, Steve
  作者单位：Carnegie Mellon University
  摘要：We study the rates of convergence in generalization error achievable by active learning under various types of label noise. Additionally, we study the general problem of model selection for active learning with a nested hierarchy of hypothesis classes and propose an algorithm whose error rate provably converges to the best achievable error among classifiers in the hierarchy at a rate adaptive to both the complexity of the optimal classifier and the noise conditions. In particular, we state suf...
• ROBUST FUNCTIONAL PRINCIPAL COMPONENTS: A PROJECTION-PURSUIT APPROACH AI翻译
  作者：Lucas Bali, Juan; Boente, Graciela; Tyler, David E.; Wang, Jane-Ling
  作者单位：University of Buenos Aires; University of California System; University of California Davis; Rutgers University System; Rutgers University New Brunswick
  摘要：In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simul...
• BERNSTEIN-VON MISES THEOREMS FOR GAUSSIAN REGRESSION WITH INCREASING NUMBER OF REGRESSORS AI翻译
  作者：Bontemps, Dominique
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
  摘要：This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of regressors increases with the sample size. Two kinds of Bernstein-von Mises theorems are obtained in this framework: nonparametric theorems for the parameter itself, and semiparametric theorems for functionals of the parameter. We apply them to the Gaussian sequ...
• NUCLEAR-NORM PENALIZATION AND OPTIMAL RATES FOR NOISY LOW-RANK MATRIX COMPLETION AI翻译
  作者：Koltchinskii, Vladimir; Lounici, Karim; Tsybakov, Alexandre B.
  作者单位：University System of Georgia; Georgia Institute of Technology; Institut Polytechnique de Paris; ENSAE Paris
  摘要：This paper deals with the trace regression model where n entries or linear combinations of entries of an unknown m(1) x m(2) matrix A(0) corrupted by noise are observed. We propose a new nuclear-norm penalized estimator of A(0) and establish a general sharp oracle inequality for this estimator for arbitrary values of n, m(1), m(2) under the condition of isometry in expectation. Then this method is applied to the matrix completion problem. In this case, the estimator admits a simple explicit fo...
• PARAMETRIC OR NONPARAMETRIC? A PARAMETRICNESS INDEX FOR MODEL SELECTION AI翻译
  作者：Liu, Wei; Yang, Yuhong
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike's information criterion (AIC) performs well in an asymptotic efficiency when the true model is infinite dimensional (nonparametric scenario). But there is little work that addresses if it is possible and how to detect the situation ...
• ASYMPTOTIC BAYES-OPTIMALITY UNDER SPARSITY OF SOME MULTIPLE TESTING PROCEDURES AI翻译
  作者：Bogdan, Malgorzata; Chakrabarti, Arijit; Frommlet, Florian; Ghosh, Jayanta K.
  作者单位：Wroclaw University of Science & Technology; University of Vienna; Indian Statistical Institute; Indian Statistical Institute Kolkata; Purdue University System; Purdue University
  摘要：Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model and the total loss is assumed to be the sum of losses for individual tests. Our model can be used for testing point null hypotheses, as well as to distinguish large signals from a multitude of very small effects. A rule is defined to be asymptotically Bayes o...
• THE EFM APPROACH FOR SINGLE-INDEX MODELS AI翻译
  作者：Cui, Xia; Haerdle, Wolfgang Karl; Zhu, Lixing
  作者单位：Sun Yat Sen University; Humboldt University of Berlin; Hong Kong Baptist University; National Central University; Yunnan University of Finance & Economics
  摘要：Single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, parallel to beta parallel to = 1, represents a nonregul...
• BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY AI翻译
  作者：Goldenshluger, Alexander; Lepski, Oleg
  作者单位：University of Haifa; Aix-Marseille Universite
  摘要：We address the problem of density estimation with L(s)(-)loss by selection of kernel estimators. We develop a selection procedure and derive corresponding L-s-risk oracle inequalities. It is shown that the proposed selection rule leads to the estimator being minimax adaptive over a scale of the anisotropic Nikol'skii classes. The main technical tools used in our derivations are uniform bounds on the L-s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (...