5期

最新文章

• REGULARIZED RANK-BASED ESTIMATION OF HIGH-DIMENSIONAL NONPARANORMAL GRAPHICAL MODELS AI翻译
  作者：Xue, Lingzhou; Zou, Hui
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in many applications. However, in practice we often face nonnormal data, and variable transformation is often used to achieve normality. In this paper we consider the nonparanormal model that assumes that the variables follow a joint normal distribut...
• ESTIMATION IN FUNCTIONAL REGRESSION FOR GENERAL EXPONENTIAL FAMILIES AI翻译
  作者：Dou, Winston Wei; Pollard, David; Zhou, Harrison H.
  作者单位：Yale University
  摘要：This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equiv...
• A PENALIZED EMPIRICAL LIKELIHOOD METHOD IN HIGH DIMENSIONS AI翻译
  作者：Lahiri, Soumendra N.; Mukhopadhyay, Subhadeep
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely de...
• NONPARAMETRIC REGRESSION FOR LOCALLY STATIONARY TIME SERIES AI翻译
  作者：Vogt, Michael
  作者单位：University of Cambridge
  摘要：In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes ...
• JOINT VARIABLE AND RANK SELECTION FOR PARSIMONIOUS ESTIMATION OF HIGH-DIMENSIONAL MATRICES AI翻译
  作者：Bunea, Florentina; She, Yiyuan; Wegkamp, Marten H.
  作者单位：Cornell University; State University System of Florida; Florida State University; Cornell University
  摘要：We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-dimensional approximations of the parameter matrix in such models. We show in this article that important gains in prediction accuracy can be obtained by considering them jointly....
• FAST GLOBAL CONVERGENCE OF GRADIENT METHODS FOR HIGH-DIMENSIONAL STATISTICAL RECOVERY AI翻译
  作者：Agarwal, Alekh; Negahban, Sahand; Wainwright, Martin J.
  作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
  摘要：Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framework that allows the ambient dimension d to grow with (and possibly exceed) the sample size n. Our theory identifies conditions under which projected gradient descent enjoys globally ...
• OPTIMAL WEIGHTED NEAREST NEIGHBOUR CLASSIFIERS AI翻译
  作者：Samworth, Richard J.
  作者单位：University of Cambridge
  摘要：We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has a rather simple form. We show that the ratio of the regret of this classifier to that of an unweighted k-nearest neighbour classifier depends asymptotically only on the dimension d of the feature vectors, and not on the underlying populations. The improvement is greatest when d = 4, but thereafter d...
• ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATION IN MISSPECIFIED HIDDEN MARKOV MODELS AI翻译
  作者：Douc, Randal; Moulines, Eric
  作者单位：IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique
  摘要：Let (Y-k)(k is an element of Z) be a stationary sequence on a probability space (Omega, A, P) taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Y-k)(k is an element of Z) is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under m...
• TIGHT CONDITIONS FOR CONSISTENCY OF VARIABLE SELECTION IN THE CONTEXT OF HIGH DIMENSIONALITY AI翻译
  作者：Comminges, Laetitia; Dalalyan, Arnak S.
  作者单位：Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Institut Polytechnique de Paris; ENSAE Paris
  摘要：We address the issue of variable selection in the regression model with very high ambient dimension, that is, when the number of variables is very large. The main focus is on the situation where the number of relevant variables, called intrinsic dimension, is much smaller than the ambient dimension d. Without assuming any parametric form of the underlying regression function, we get tight conditions making it possible to consistently estimate the set of relevant variables. These conditions rel...
• SAMPLED FORMS OF FUNCTIONAL PCA IN REPRODUCING KERNEL HILBERT SPACES AI翻译
  作者：Amini, Arash A.; Wainwright, Martin J.
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from H to R-m, where the functional components to lie in some Hilbert subspace H of L-2, such as a reproducing kernel Hilbert space of smooth functions. This model includes time and frequency sampling as special cases. In contrast to classical approach in fPCA...