The Annals of Statistics

最新文章

• ASYMPTOTIC DISTRIBUTIONS OF LARGEST PEARSON CORRELATION COEFFICIENTS UNDER DEPENDENT STRUCTURES AI翻译
  作者：Jiang, Tiefeng; Pham, Tuan
  作者单位：The Chinese University of Hong Kong, Shenzhen; University of Texas System; University of Texas Austin
  摘要：Given a random sample from a multivariate normal distribution whose covariance matrix is a Toeplitz matrix, we study the largest off-diagonal entry of the sample correlation matrix. Assuming the multivariate normal distribution has the covariance structure of an autoregressive sequence, we establish a phase transition in the limiting distribution of the largest off-diagonal entry. We show that the limiting distributions are of Gumbel-type (with different parameters), depending on how large or ...
• ASYMPTOTIC EQUIVALENCE OF LOCALLY STATIONARY PROCESSES AND BIVARIATE GAUSSIAN WHITE NOISE AI翻译
  作者：Butucea, Cristina; Meister, Alexander; Rohde, Angelika
  作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Rostock; University of Freiburg
  摘要：We consider a general class of statistical experiments, in which an ndimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be well-approximable in a linear space of lower dimension Kn with eigenvalues uniformly bounded away from zero and infinity. We prove asymptotic equivalence of this experiment and a class of Kn-dimensional Gaussian models with informative expectation in Le Cam's sense when n ten...
• RESIDUAL PERMUTATION TEST FOR REGRESSION COEFFICIENT TESTING AI翻译
  作者：Wen, Kaiyue; Wang, Tengyao; Wang, Yuhao
  作者单位：Stanford University; University of London; London School Economics & Political Science; Tsinghua University
  摘要：We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates p can be up to a constant fraction of sample size n. In this regime, an important topic is to propose tests with finite-sample valid size control without requiring the noise to follow strong distributional assumptions. In this paper, we propose a new method, called the residual permutation test (RPT), which is constructed by projecting the regression residuals onto...
• LARGE-DIMENSIONAL INDEPENDENT COMPONENT ANALYSIS: STATISTICAL OPTIMALITY AND COMPUTATIONAL TRACTABILITY AI翻译
  作者：Auddy, Arnab; Yuan, Ming
  作者单位：University System of Ohio; Ohio State University; Columbia University
  摘要：In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality on sample complexity and statistical accuracy, and how computational consideration may affect them. In particular, we show that the optimal sample complexity is linear in dimensionality, and interestingly, the commonly used sample kurtosis-based approaches ...
• A DUALITY FRAMEWORK FOR ANALYZING RANDOM FEATURE AND TWO-LAYER NEURAL NETWORKS AI翻译
  作者：Chen, Hongrui; Long, Jihao; Wu, Lei
  作者单位：Stanford University; Peking University
  摘要：We consider the problem of learning functions within the Fp,pi and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks as well as kernel methods. Leveraging tools from information-based complexity (IBC), we establish a dual equivalence between approximation and estimation and then apply it to study the learning of the preceding function spaces. The duality allows us to focus on the more tractable problem between approximation and est...
• BAYESIAN NONPARAMETRIC INFERENCE IN MCKEAN-VLASOV MODELS AI翻译
  作者：Nickl, Richard; Pavliotis, Grigorios A.; Ray, Kolyan
  作者单位：University of Cambridge; Imperial College London
  摘要：We consider nonparametric statistical inference on a periodic interaction potential W from noisy discrete space-time measurements of solutions rho = rho W of the nonlinear McKean-Vlasov equation, describing the probability density of the mean field limit of an interacting particle system. We show how Gaussian process priors assigned to W give rise to posterior mean estimators that exhibit fast convergence rates for the implied estimated densities rho towards rho W . We further show that if the...
• MULTIVARIATE DYNAMIC MEDIATION ANALYSIS UNDER A REINFORCEMENT LEARNING FRAMEWORK AI翻译
  作者：Luo, Lan; Shi, Chengchun; Wang, Jitao; Wi, Zhenke; Li, Lexin
  作者单位：Rutgers University System; Rutgers University New Brunswick; University of London; London School Economics & Political Science; University of Michigan System; University of Michigan; University of California System; University of California Berkeley
  摘要：Mediation analysis is an important analytic tool commonly used in a broad range of scientific applications. In this article, we study the problem of mediation analysis when there are multivariate and conditionally dependent mediators, and when the variables are observed over multiple time points. The problem is challenging, because the effect of a mediator involves not only the path from the treatment to this mediator itself at the current time point, but also all possible paths pointed to thi...
• CONCENTRATION OF DISCREPANCY-BASED APPROXIMATE BAYESIAN COMPUTATION VIA RADEMACHER COMPLEXITY AI翻译
  作者：Legramanti, Sirio; Durante, Daniele; Alquier, Pierre
  作者单位：University of Bergamo; Bocconi University; Bocconi University; ESSEC Business School
  摘要：There has been an increasing interest on summary-free solutions for approximate Bayesian computation (ABC) that replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these strategies has motivated theoretical studies on the limiting properties of the induced posteriors. However, there is still the lack of a theoretical framework for summary-free ABC th...
• TESTING STATIONARITY AND CHANGE POINT DETECTION IN REINFORCEMENT LEARNING AI翻译
  作者：Li, Mengbing; Shi, Chengchun; Wu, Zhenke; Fryzlewicz, Piotr
  作者单位：University of Michigan System; University of Michigan; University of London; London School Economics & Political Science
  摘要：We consider reinforcement learning (RL) in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the state transition and reward functions to be constant over time. However, this assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a model-free test to assess the stationarity of the opti...
• CONFORMAL INFERENCE FOR RANDOM OBJECTS AI翻译
  作者：Zhou, Hang; Mueller, Hans-Georg
  作者单位：University of California System; University of California Davis
  摘要：We develop an inferential tool kit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end, we introduce conditional profile average transport costs, where we compare distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius through the optimal transport cost when moving from one distance profile to another....