The Annals of Statistics

最新文章

• MODEL SELECTION IN THE SPACE OF GAUSSIAN MODELS INVARIANT BY SYMMETRY AI翻译
  作者：Graczyk, Piotr; Ishi, Hideyuki; Kolodziejek, Bartosz; Massam, Helene
  作者单位：Universite d'Angers; Osaka Metropolitan University; Warsaw University of Technology; York University - Canada
  摘要：We consider multivariate centered Gaussian models for the random variable Z = (Z(1),..., Z(p)), invariant under the action of a subgroup of the group of permutations on {1,..., p}. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter Sigma and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter K = Sigma(-1...
• PARAMETRIC COPULA ADJUSTED FOR NON- AND SEMIPARAMETRIC REGRESSION AI翻译
  作者：Zhao, Yue; Gijbels, Irene; Van Keilegom, Ingrid
  作者单位：KU Leuven; KU Leuven; KU Leuven; University of York - UK
  摘要：We consider a multivariate response regression model where each coordinate is described by a location-scale non- or semiparametric regression and where the dependence structure of the noise term is described by a parametric copula. Our goal is to estimate the associated Euclidean copula parameter, given a sample of the response and the covariate. In the absence of the copula sample, the usual oracle ranks are no longer computable. Instead, we study the normal scores estimator for the Gaussian ...
• APPROXIMATE MESSAGE PASSING ALGORITHMS FOR ROTATIONALLY INVARIANT MATRICES AI翻译
  作者：Fan, Zhou
  作者单位：Yale University
  摘要：Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational invariance in law,...
• TESTING FOR THE RANK OF A COVARIANCE OPERATOR AI翻译
  作者：Charkaborty, Anirvan; Panaretos, Victor M.
  作者单位：Indian Institute of Science Education & Research (IISER) - Kolkata; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional data, which require low-dimensional representa-tions whether by functional PCA or other methods. The difficulty is that the determination is to be made on the basis of i.i.d. replications of the process observed discretely and with measurement e...
• THE COMPLETION OF COVARIANCE KERNELS AI翻译
  作者：Waghmare, Kartik G.; Panaretos, Victor M.
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega called serrated domains, we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of the canon...
• NEW EDGEWORTH-TYPE EXPANSIONS WITH FINITE SAMPLE GUARANTEES AI翻译
  作者：Zhilova, Mayya
  作者单位：University System of Georgia; Georgia Institute of Technology
  摘要：We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean balls and the set of all half-spaces. These results allow to account for an impact of higher-order moments or cumulants of the considered distributions; the obtained error terms depend on a sample size and a dimension explicitly. The new inequalities outperfo...
• ON THE ROBUSTNESS OF MINIMUM NORM INTERPOLATORS AND REGULARIZED EMPIRICAL RISK MINIMIZERS AI翻译
  作者：Chinot, Geoffrey; Loeffler, Matthias; van de Geer, Sara
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on the errors are imposed. A quantitative bound for the prediction error is given, relating it to the Rademacher complexity of the covariates, the norm of the minimum norm interpolator of the errors and the size of the subdifferential around the true parameter...
• CONSISTENCY OF INVARIANCE-BASED RANDOMIZATION TESTS AI翻译
  作者：Dobriban, Edgar
  作者单位：University of Pennsylvania
  摘要：Invariance-based randomization tests-such as permutation tests, rotation tests, or sign changes-are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data distribution. Most work focuses on their type I error control properties, while their consistency properties are much less understood. We develop a general framework to study the consistency of invariance-based randomization tests, assuming the data is drawn from a signal-p...
• LEARNING MIXTURES OF PERMUTATIONS: GROUPS OF PAIRWISE COMPARISONS AND COMBINATORIAL METHOD OF MOMENTS AI翻译
  作者：Mao, Cheng; Wu, Yihong
  作者单位：University System of Georgia; Georgia Institute of Technology; Yale University
  摘要：In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we propose a polynomial-time algorithm that learns a Mallows mixture of permutations on n elements with the optimal sample complexity that is proportional to log n, improving upon previous results that scale polynomially with n. In the high-noise regime, we charact...
• EXACT MINIMAX RISK FOR LINEAR LEAST SQUARES, AND THE LOWER TAIL OF SAMPLE COVARIANCE MATRICES AI翻译
  作者：Mourtada, Jaouad
  作者单位：Institut Polytechnique de Paris; ENSAE Paris
  摘要：We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order d/n in dimension d with n samples. Here, we study the minimax expected excess risk over the full linear class, depending on the distribution of covariates. First, the least squares estimator is exactly minimax optimal in the well-specified case, for every distribution of covariates. We express the minimax risk in t...