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作者：Zou, Nan; Volgushev, Stanislav; Buecher, Axel
作者单位：University of Toronto; Heinrich Heine University Dusseldorf
摘要：Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from different blocks are dependent. Theory respecting the latter complications is not well developed, and, in the multivariate case, has only recently bee...
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作者：Barber, Rina Foygel; Candes, Emmanuel J.; Ramdas, Aaditya; Tibshirani, Ryan J.
作者单位：University of Chicago; Stanford University; Stanford University; Carnegie Mellon University; Carnegie Mellon University
摘要：This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial...
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作者：Han, Qiyang; Wellner, Jon A.
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Washington; University of Washington Seattle
摘要：In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko-Cantelli and Donsker theorems, and local theorems such as local asymptotic modulus and related ratio-type limit theorems are proved for both the Horvitz-Thompson empirical process, and its calibrated version. Limit theorems of other variants and their conditional versions are also estab...
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作者：Duchi, John C.; Ruan, Feng
作者单位：Stanford University
摘要：We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hajek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our results provide function-specific lower bounds and convergence results that make precise a correspondence between statistical difficulty and the geometric notion of tilt-stabili...
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作者：Zhang, Danna; Wu, Wei Biao
作者单位：University of California System; University of California San Diego; University of Chicago
摘要：Covariances and spectral density functions play a fundamental role in the theory of time series. There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes. For high-dimensional non-stationary processes, however, many important problems on their asymptotic behaviors are still unanswered. This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of high-dimensional locally statio...
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作者：Pollak, Moshe
作者单位：Hebrew University of Jerusalem
摘要：Consider a process that produces a series of independent identically distributed vectors. A change in an underlying state may become manifest in a modification of one or more of the marginal distributions. Often, the dependence structure between coordinates is unknown, impeding surveillance based on the joint distribution. A popular approach is to construct control charts for each coordinate separately and raise an alarm the first time any (or some) of the control charts signals. The difficult...
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作者：Xia, Dong; Yuan, Ming; Zhang, Cun-Hui
作者单位：Hong Kong University of Science & Technology; Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundamental computational challenges often associated with problems involving higher order tensors, yet very little is known about their statistical performance. To fill in this void, in...
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作者：Montanari, Andrea; Venkataramanan, Ramji
作者单位：Stanford University; Stanford University; University of Cambridge
摘要：Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise, a setting that is also known as spiked model or deformed random matrix. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic accuracy of Bayes-optimal estimators in the high-dimensional limit. In this paper, we present a practical alg...
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作者：Chen, Yuxin; Cheng, Chen; Fan, Jianqing
作者单位：Princeton University; Stanford University; Princeton University
摘要：This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix M* is an element of R-n(xn), yet only a randomly perturbed version M is observed. The noise matrix M - M* is composed of independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise if, for example, when we have two independent samples for each entry of M* and arrange them in...
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作者：Obloj, Jan; Wiesel, Johannes
作者单位：University of Oxford; University of Oxford
摘要：We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. We then ext...
