The Annals of Statistics

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• RATES OF ESTIMATION FOR HIGH-DIMENSIONAL MULTIREFERENCE ALIGNMENT AI翻译
  作者：Dou, Zehao; Fan, Zhou; Zhou, Harrison H.
  作者单位：Yale University
  摘要：We study the continuous multireference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryoelectron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K. In a high-noise regime with noise variance sigma 2 >= K, for signals with Fourier coefficients of roughly uniform magnitude, the rate scales as sigma 6 and has no ...
• CHARACTERIZATION OF CAUSAL ANCESTRAL GRAPHS FOR TIME SERIES WITH LATENT CONFOUNDERS AI翻译
  作者：Gerhardus, Andreas
  作者单位：Helmholtz Association; German Aerospace Centre (DLR)
  摘要：In this paper, we introduce a novel class of graphical models for representing time-lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and show that they constitute proper subsets of the currently employed model classes. As we show, from the novel graphs one can thus draw stronger causal inferences-without additional assumptions. We further introduce a graphical representation of Markov equivalen...
• TENSOR FACTOR MODEL ESTIMATION BY ITERATIVE PROJECTION AI翻译
  作者：Han, Yuefeng; Chen, Rong; Yang, Dan; Zhang, Cun-Hui
  作者单位：University of Notre Dame; Rutgers University System; Rutgers University New Brunswick; University of Hong Kong
  摘要：Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper, we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the o...
• TIME-UNIFORM CENTRAL LIMIT THEORY AND ASYMPTOTIC CONFIDENCE SEQUENCES AI翻译
  作者：Waudby-smith, Ian; Arbour, David; Sinha, Ritwik; Kennedy, Edward H.; Ramdas, Aaditya
  作者单位：Carnegie Mellon University; Adobe Systems Inc.
  摘要：Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS)-sequences of confidence intervals that ar...
• A GENERAL FRAMEWORK TO QUANTIFY DEVIATIONS FROM STRUCTURAL ASSUMPTIONS IN THE ANALYSIS OF NONSTATIONARY FUNCTION-VALUED PROCESSES AI翻译
  作者：Van Delft, Anne; Dette, Holger
  作者单位：Columbia University; Ruhr University Bochum
  摘要：We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral density operators. The second-order dynamics are well known to be elements of the space of trace class operators, the latter is a Banach space of type 1 and of cotype 2, which makes the development of statistical inference tools more challenging. A part of our ...
• GAUSSIAN APPROXIMATION FOR NONSTATIONARY TIME SERIES WITH OPTIMAL RATE AND EXPLICIT CONSTRUCTION AI翻译
  作者：Bonnerjee, Soham; Karmakar, Sayar; Wu, Wei Biao
  作者单位：University of Chicago; State University System of Florida; University of Florida
  摘要：Statistical inference for time series such as curve estimation for time- varying models or testing for existence of a change point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for nonstationary processes only provide an existential proof, and thus they are difficult to apply. In this paper, we provide two clear paths to c...
• COMPUTATIONAL LOWER BOUNDS FOR GRAPHON ESTIMATION VIA LOW-DEGREE POLYNOMIALS AI翻译
  作者：Luo, Yuetian; Gao, Chao
  作者单位：University of Chicago; University of Chicago
  摘要：Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been established by (Ann. Statist. 43 (2015) 2624-2652) for both stochastic block model (SBM) and nonparametric graphon estimation. The statistical optimal estimators are based on constrained least squares and have computational complexity exponential in the dimension. ...
• ONE-STEP ESTIMATION OF DIFFERENTIABLE HILBERT-VALUED PARAMETERS AI翻译
  作者：Luedtke, Alex; Chung, Incheoul
  作者单位：University of Washington; University of Washington Seattle
  摘要：We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient, root-n n rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimato...
• STEREOGRAPHIC MARKOV CHAIN MONTE CARLO AI翻译
  作者：Yang, Jun; Latuszynski, Krzysztof; Roberts, Gareth o.
  作者单位：University of Copenhagen; University of Warwick
  摘要：High-dimensional distributions, especially those with heavy tails, are results in empirically observed stickiness and poor theoretical mixing properties-lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of the Bouncy Particle Sampler that are uniformly...
• MULTIVARIATE TREND FILTERING FOR LATTICE DATA AI翻译
  作者：Sadhanala, Veeranjaneyulu; Wang, Yu-xiang; Hu, Addison j.; Tibshirani, Ryan j.
  作者单位：Alphabet Inc.; Google Incorporated; University of California System; University of California San Diego; Carnegie Mellon University; University of California System; University of California Davis
  摘要：We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in d dimensions. KTF is a natural extension of univariate trend filtering ( Int. J. Comput. Vis. 70 (2006) 214-255; SIAM Rev. 51 (2009) 339-360; Ann. Statist. 42 (2014) 285-323), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be estimated along each ...