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作者：Cai, T. Tony; Wang, Yichen; Zhang, Linjun
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
摘要：Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the (s, 8)-differential privacy...
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作者：Castillo, Ismael; van der Pas, Stephanie
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Vrije Universiteit Amsterdam; University of Amsterdam
摘要：We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for 'many' functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein-von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, w...
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作者：Yuan, Yubai; Qu, Annie
作者单位：University of California System; University of California Irvine
摘要：In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate intracommunity dependence of connectivities through the Bahadur representat...
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作者：Han, Qiyang
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper bound for the convergence rates thus obtained typically matches the minimax lower bound when the entropy integral converges, but admits a strict gap compared to the lower bound when it diverges. Birge and Massart (Probab. Theory Related Fields 97 (1993) 113...
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作者：Ortelli, Francesco; van de Geer, Sara
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of (k - 1)th order differences. Our approach is based on combining a general oracle inequality for the l(1)-penalized least squares estimator with interpolating vectors to upper bound the effective sparsity. This allows one to show that the l(1)-penalty on the kth order differences leads to an estimator that can adapt to the number of jumps in the (k - 1)th order differences of the...
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作者：Wang, Chunyan; Mee, Robert W.
作者单位：Nankai University; Nankai University; University of Tennessee System; University of Tennessee Knoxville
摘要：Regular 2(n-P) designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to f-PFD with f > 3 is more challenging. This paper aims to study the general theory for the f-PFD for any f >= 3. We propose a method for obtaining the confounding frequency vectors for all nonequivalent f-PFDs, and to find the least G-aberration (or highest D-efficiency) f-PFD...
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作者：Belomestny, Denis; Goldenshluger, Alexander
作者单位：University of Duisburg Essen; University of Haifa; HSE University (National Research University Higher School of Economics)
摘要：In this paper, we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically, deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the characteristic function of the measurement errors does not have zeros on the real line. This assumption is rather strong and is not fulfilled in many cases of interest. In this paper, we develop a methodology for constructing optimal density deconvolution e...
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作者：Cai, T. Tony; Wei, Hongji
作者单位：University of Pennsylvania
摘要：Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first establish the minimax r...
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：Nonparametric estimation of the cumulative distribution function and the probability density of a lifetime X modified by a current status censoring (CSC), including cases of right and left missing data, is a classical ill-posed problem with biased data. The biased nature of CSC data may preclude us from consistent estimation unless the biasing function is known or may be estimated, and its ill-posed nature slows down rates of convergence. Under a traditionally studied CSC, we observe a sample ...
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作者：Girard, Stephane; Stupfler, Gilles; Usseglio-Carleve, Antoine
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Inria; Institut National Polytechnique de Grenoble; Centre National de la Recherche Scientifique (CNRS); Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Universite de Rennes; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regre...
