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作者：Zhang, Yi; Shao, Xiaofeng; Wu, Weibiao
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago
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作者：Cai, T. Tony; Wei, Hongji
作者单位：University of Pennsylvania
摘要：Distributed estimation of a Gaussian mean with unknown variance under communication constraints is studied. Necessary and sufficient communication costs under different types of distributed protocols are derived for any estimator that is adaptively rate-optimal over a range of possible values for the variance. Communication-efficient and statistically optimal procedures are developed. The analysis reveals an interesting and important distinction among different types of distributed protocols: ...
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作者：Chzhen, Evgenii; Schreuder, Nicolas
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Genoa
摘要：We propose a theoretical framework for the problem of learning a real-valued function which meets fairness requirements. This framework is built upon the notion of alpha-relative (fairness) improvement of the regression function which we introduce using the theory of optimal transport. Setting alpha = 0 corresponds to the regression problem under the Demographic Parity constraint, while alpha = 1 corresponds to the classical regression problem without any constraints. For alpha is an element o...
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作者：Bhattacharya, Bhaswar B.; Das, Sayan; Mukherjee, Sumit
作者单位：University of Pennsylvania; Columbia University; Columbia University
摘要：Network sampling is an indispensable tool for understanding features of large complex networks where it is practically impossible to search over the entire graph. In this paper, we develop a framework for statistical inference for counting network motifs, such as edges, triangles and wedges, in the widely used subgraph sampling model, where each vertex is sampled independently, and the subgraph induced by the sampled vertices is observed. We derive necessary and sufficient conditions for the c...
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作者：Ghosal, Promit; Sen, Bodhisattva
作者单位：Massachusetts Institute of Technology (MIT); Columbia University
摘要：In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al. (Ann. Statist. 45 (2017) 223-256) and Hallin et al. (Ann. Statist. 49 (2021) 1139-1165). We study the characterization, computation and properties of the multivariate rank and quantile functions and their empirical counterparts. We derive the uniform consistency of these empirical estimates to their population versions, under certain assumptions....
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作者：Banerjee, Debapratim; Ma, Zongming
作者单位：University of Pennsylvania
摘要：We study signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked cases in these models and with flexible priors on signal components that allow dependence across spikes. We derive asymptotic normality for the log-likelihood ratios when the signal-to-noise ratios are below certain bounds. In addition, the log-likelihood ratios can be asymptotic...
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作者：Stoltenberg, Emil A.; Mykland, Per A.; Zhang, Lan
作者单位：BI Norwegian Business School; University of Chicago; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：In this paper, we introduce a general method for estimating the quadratic covariation of one or more spot parameter processes associated with continuous time semimartingales, and present a central limit theorem that has this class of estimators as one of its applications. The class of estimators we introduce, that we call Two-Scales Quadratic Covariation (TSQC) estimators, is based on sums of increments of second differences of the observed processes, and the intervals over which the differenc...
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作者：Chen, Yaqing; Muller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Local Frechet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to ...
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作者：Lauritzen, Steffen; Zwiernik, Piotr
作者单位：University of Copenhagen; University of Toronto
摘要：The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper, we propose a concept of local association, where highly connected components in a graphical model are positively associated and study its properties. Our main motivation comes from gene expression data, where graphical models have become a popular exploratory tool. The models are instances of what we term mixed convex exponential familie...
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作者：Bykhovskaya, Anna; Gorin, Vadim
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from overrejection. This is a...
