5期

最新文章

• SPATIALLY INHOMOGENEOUS LINEAR INVERSE PROBLEMS WITH POSSIBLE SINGULARITIES AI翻译
  作者：Pensky, Marianna
  作者单位：State University System of Florida; University of Central Florida
  摘要：The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator Q depends not only on the scale but also on location. In this case, the rates of convergence are determined by the interaction of four parameters, the smoothness and spatial homogeneity of the unknown function f and degrees of ill-posedness and spatial inhomogeneity of operator Q. Estimators obtained in the paper are based either on wa...
• ASYMPTOTIC EQUIVALENCE OF QUANTUM STATE TOMOGRAPHY AND NOISY MATRIX COMPLETION AI翻译
  作者：Wang, Yazhen
  作者单位：University of Wisconsin System; University of Wisconsin Madison
  摘要：Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. R...
• CONVERGENCE RATES OF EIGENVECTOR EMPIRICAL SPECTRAL DISTRIBUTION OF LARGE DIMENSIONAL SAMPLE COVARIANCE MATRIX AI翻译
  作者：Xia, Ningning; Qin, Yingli; Bai, Zhidong
  作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; University of Waterloo
  摘要：The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Marcenko-Pastur distribution function is of order O(N-1/2). Given that data dimension n to sample size N ratio is bounded between 0 and 1, this convergence rate is established under finite 10th moment condition of the u...
• LOCAL AND GLOBAL ASYMPTOTIC INFERENCE IN SMOOTHING SPLINE MODELS AI翻译
  作者：Shang, Zuofeng; Cheng, Guang
  作者单位：University of Notre Dame; Purdue University System; Purdue University
  摘要：This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577-580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii) local likelihood ratio...
• OPTIMAL CLASSIFICATION IN SPARSE GAUSSIAN GRAPHIC MODEL AI翻译
  作者：Fan, Yingying; Jin, Jiashun; Yao, Zhigang
  作者单位：University of Southern California; Carnegie Mellon University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix Sigma, where the precision matrix Omega = Sigma(-1) is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of Omega, we formulate the setting as a linear regre...
• EQUIVALENCE OF DISTANCE-BASED AND RKHS-BASED STATISTICS IN HYPOTHESIS TESTING AI翻译
  作者：Sejdinovic, Dino; Sriperumbudur, Bharath; Gretton, Arthur; Fukumizu, Kenji
  作者单位：University of London; University College London; University of Cambridge; Max Planck Society; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
  摘要：We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a positive definite ke...
• A TEST FOR THE RANK OF THE VOLATILITY PROCESS: THE RANDOM PERTURBATION APPROACH AI翻译
  作者：Jacod, Jean; Podolskij, Mark
  作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ruprecht Karls University Heidelberg
  摘要：In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.
• CALIBRATING NONCONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION AI翻译
  作者：Wang, Lan; Kim, Yongdai; Li, Runze
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; Seoul National University (SNU); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
  摘要：We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not gua...
• THE ASYMPTOTICS OF RANKING ALGORITHMS AI翻译
  作者：Duchi, John C.; Mackey, Lester; Jordan, Michael I.
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Stanford University
  摘要：We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and more practical appro...
• QUANTIFYING CAUSAL INFLUENCES AI翻译
  作者：Janzing, Dominik; Balduzzi, David; Grosse-Wentrup, Moritz; Schoelkopf, Bernhard
  作者单位：Max Planck Society; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between n variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other n - 1 variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength...