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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...
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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...
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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 ...
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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...
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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. ...
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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...
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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...
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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 ...
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作者：Niu, By ziang; Chakraborty, Abhinav; Dukes, Oliver; Katsevich, Eugene
作者单位：University of Pennsylvania; Ghent University
摘要：Model-X approaches to testing conditional independence between a predictor and an outcome variable given a vector of covariates usually assume exact knowledge of the conditional distribution of the predictor given the covariates. Nevertheless, model-X methodologies are often deployed with this conditional distribution learned in sample. We investigate the consequences of this choice through the lens of the distilled conditional randomization test (dCRT). We find that Type-I error control is st...
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作者：Chang, Jinyuan; Hu, Qiao; Kolaczyk, Eric d.; Yao, Qiwei; Yi, Fengting
作者单位：Southwestern University of Finance & Economics - China; Chinese Academy of Sciences; McGill University; University of London; London School Economics & Political Science; Yunnan University
摘要：A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here, we conduct an indepth study of this trade-off for parameter estimation in the beta-model (Ann. Appl. Probab. 21 (2011) 1400-1435) for edge differentially private network 500). Unlike most previous approaches based on maximum likelihood estimation for this network model, we proceed via the method of moments. This choice facilitates our exploration of a substantia...
