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作者：Bercu, Bernard; Bigot, Jeremie
作者单位：Universite de Bordeaux; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is devoted to the stochastic approximation of entropically regularized-Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal transportation problems can be rewritten as a nonstrongly concave optimisation problem. It allows to implement a Robbins-Monro stochastic algorithm to estimate the Sinkhorn divergence using a sequence of data sampled from one of the two distributions. Our main contribut...
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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：Buecher, Axel; Dette, Holger; Heinrichs, Florian
作者单位：Heinrich Heine University Dusseldorf; Ruhr University Bochum
摘要：Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be nonrelevant (i.e., small), or relevant for a specific problem at hand, and the present paper presents statistical methodology to detect the latt...
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作者：Einmahl, John H. J.; Segers, Johan
作者单位：Tilburg University; Tilburg University
摘要：For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to continuous functio...
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作者：Panigrahi, Snigdha; Taylor, Jonathan; Weinstein, Asaf
作者单位：University of Michigan System; University of Michigan; Stanford University; Hebrew University of Jerusalem
摘要：Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently on large and useful classes of problems by harnessing general theory of hypothesis testing in exponential families, but these methods have their limitations. Perhaps most immediate is the gap between theory and practice: implementing the exact theoretical pre...
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作者：Deng, Hang; Han, Qiyang; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, Han and Zhang (2020) obtained a pointwise limit distribution theory for the so-called block maxmin and min-max estimators (Fokianos, Leucht and Neumann (2020); Deng and Zhang (2020)) in this model, but inference remains a difficult problem due to the nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the true regression func...
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作者：Chernozhukov, Victor; Haerdle, Wolfgang Karl; Huang, Chen; Wang, Weining
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Humboldt University of Berlin; Aarhus University; CREATES; Aarhus University; University of York - UK
摘要：We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for...
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作者：Liu, Haoyang; Gao, Chao; Samworth, Richard J.
作者单位：University of Chicago; University of Cambridge
摘要：We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for n independent, p-variate Gaussian observations. This rate exhibits a phase transition when the sparsity level is of order root p log log (8n) and has a very delicate dependence on the sample size: in a certain sparsity regime, it involves a triple iterated logarithmic factor in n. Furth...
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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...
