The Annals of Statistics

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• DEEP NONPARAMETRIC REGRESSION ON APPROXIMATE MANIFOLDS: NONASYMPTOTIC ERROR BOUNDS WITH POLYNOMIAL PREFACTORS AI翻译
  作者：Jiao, Yuling; Shen, Guohao; Liu, Yuanyuan; Huang, Jian
  作者单位：Wuhan University; Hong Kong Polytechnic University; Chinese University of Hong Kong
  摘要：We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the exist-ing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent the curse of dime...
• ON ROBUSTNESS AND LOCAL DIFFERENTIAL PRIVACY AI翻译
  作者：Li, Mengchu; Berrett, Thomas B.; Yu, Yi
  作者单位：University of Warwick
  摘要：It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local dif-ferential privacy (LDP) constraints.In this paper, we start with a general minimax lower bound result, which di...
• PAIRWISE INTERACTION FUNCTION ESTIMATION OF STATIONARY GIBBS POINT PROCESSES USING BASIS EXPANSION AI翻译
  作者：Ba, Ismaila; Coeurjolly, Jean-Francois; Cuevas-Pacheco, Francisco
  作者单位：University of Quebec; University of Quebec Montreal; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Universidad Tecnica Federico Santa Maria
  摘要：The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern x and a loca-tion u, is roughly speaking the probability that an event occurs in an infinites-imal ball around u given the rest of the configuration is x. The most simple and natural class of models is the class of pairwise interaction point processes where the conditional int...
• FINITE-SAMPLE COMPLEXITY OF SEQUENTIAL MONTE CARLO ESTIMATORS AI翻译
  作者：Marion, Joe; Mathews, Joseph; Schmidler, Scott C.
  作者单位：Duke University
  摘要：We present bounds for the finite-sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite-sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions such as finite spaces...
• ON THE DISJOINT AND SLIDING BLOCK MAXIMA METHOD FOR PIECEWISE STATIONARY TIME SERIES AI翻译
  作者：Buecher, Axel; Zanger, Leandra
  作者单位：Heinrich Heine University Dusseldorf
  摘要：Modeling univariate block maxima by the generalized extreme value dis-tribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying station-ary time series, respective estimators may be improved by calculating block maxima in an overlapping way. A proof of concept is provided that the lat-ter finding also holds in situations that involve certain piecewise stationari-ties. A weak convergence result for an empirica...
• RELAXING THE IID ASSUMPTION: ADAPTIVELY MINIMAX OPTIMAL REGRET VIA ROOT-ENTROPIC REGULARIZATION AI翻译
  作者：Bilodeau, Blair; Negrea, Jeffrey; Roy, Daniel M.
  作者单位：University of Toronto; University of Waterloo
  摘要：We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semiadversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm-long known to be minimax (rate) optimal in the adversarial regime-was recently shown to ...
• TOTAL POSITIVITY IN MULTIVARIATE EXTREMES AI翻译
  作者：Roettger, Frank; Engelke, Sebastian; Zwiernik, Piotr
  作者单位：University of Geneva; University of Toronto
  摘要：Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 (MTP2) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce EMTP2, an extremal version of MTP2. This notion turns out to appear prominently in extremes, and in fact, i...
• INFERENCE FOR EXTREMAL REGRESSION WITH DEPENDENT HEAVY-TAILED DATA AI翻译
  作者：Daouia, Abdelaati; Stupfler, Gilles; Usseglio-carleve, Antoine
  作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite d'Angers; Avignon Universite
  摘要：Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. We develop a fully operational inferential theory for extreme conditional quantiles and expectiles in the challenging framework of alpha-mixing, conditional heavy-tailed data whose tail index may vary with covariate values. This requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling difficulties inherent t...
• ON BACKWARD SMOOTHING ALGORITHMS AI翻译
  作者：Dau, Hai-dang; Chopin, Nicolas
  作者单位：Institut Polytechnique de Paris; ENSAE Paris
  摘要：In the context of state-space models, skeleton-based smoothing algo-rithms rely on a backward sampling step, which by default, has a O(N-2) complexity (where N is the number of particles). Existing improvements in the literature are unsatisfactory: a popular rejection sampling-based approach, as we shall show, might lead to badly behaved execution time; another rejec-tion sampler with stopping lacks complexity analysis; yet another MCMC-inspired algorithm comes with no stability guarantee. We ...
• A CROSS-VALIDATION FRAMEWORK FOR SIGNAL DENOISING WITH APPLICATIONS TO TREND FILTERING, DYADIC CART AND BEYOND AI翻译
  作者：Chaudhuri, Anamitra; Chatterjee, Sabyasachi
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting crossvalidated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the generality of the f...