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作者：Kong, Xiangshun; Yuan, Mingao; Zheng, Wei
作者单位：Beijing Institute of Technology; North Dakota State University Fargo; University of Tennessee System; University of Tennessee Knoxville
摘要：This paper considers both approximate and exact designs for estimating the total effects under one crossover and two interference models. They are different from the traditional block designs in the sense that the assigned treatments also affect their neighboring plots, hence a design is understood as a collection of sequences of treatments. A notable result in literature is that the circular neighbor balanced design (CNBD) is optimal among designs, which do not allow treatments to be neighbor...
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作者：Chandler, Gabriel; Polonik, Wolfgang
作者单位：Claremont Colleges; Pomona College; University of California System; University of California Davis
摘要：A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. Based on geometric considerations, we map each pair of data points into a real-valued feature function defined on the unit interval. Further statistical analysis is then based on the collection of feature functions. The potential of the method is illustrated by different applications, including classification and anomaly detection. Connections to other concepts, such as random set theory, localize...
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作者：Amini, Arash A.; Razaee, Zahra S.
作者单位：University of California System; University of California Los Angeles; Cedars Sinai Medical Center
摘要：We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions on R-d, including the strongly log-concave distributions under affine transformations. A feature of our result is that the data points need not have identical distributions or zero mean, which is key in certain applications such as clustering. Ou...
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作者：Caponera, Alessia; Marinucci, Domenico
作者单位：Sapienza University Rome; University of Rome Tor Vergata
摘要：In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in mean-square and sup norm), then a quantitative central limit theorem (in Wasserstein distance), and finally a weak convergence result, under more restrictive regularity conditions. Our results are validated by a small numerical investigation.
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作者：Lin, Qian; Li, Xinran; Huang, Dongming; Liu, Jun S.
作者单位：Tsinghua University; University of Illinois System; University of Illinois Urbana-Champaign; National University of Singapore; Harvard University
摘要：The central subspace of a pair of random variables (y, x) is an element of Rp+1 is the minimal subspace S such that y perpendicular to x vertical bar P(S)x. In this paper, we consider the minimax rate of estimating the central space under the multiple index model y = f(beta(tau)(1) x, beta(tau)(d), ..., beta(tau)(d)x,is an element of) with at most s active predictors, where x similar to N(0, Sigma) for some class of Sigma. We first introduce a large class of models depending on the smallest no...
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作者：Miolane, Leo; Montanari, Andrea
作者单位：New York University; New York University; Stanford University; Stanford University
摘要：The Lasso is a popular regression method for high-dimensional problems in which the number of parameters theta(1), ..., theta(N), is larger than the number n of samples: N > n. A useful heuristics relates the statistical properties of the Lasso estimator to that of a simple soft-thresholding denoiser, in a denoising problem in which the parameters (theta(i))(i <= N) are observed in Gaussian noise, with a carefully tuned variance. Earlier work confirmed this picture in the limit n, N -> infinit...
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作者：Carpentier, Alexandra; Delattre, Sylvain; Roquain, Etienne; Verzelen, Nicolas
作者单位：Otto von Guericke University; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Universite de Montpellier; INRAE; Institut Agro; Montpellier SupAgro
摘要：We introduce one-sided versions of Huber's contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of the uncorrupted samples (minimum effect) and selection of the corrupted samples (outliers). Regarding estimation of the minimum effect, we derive the minimax risks and introduce estimators that are adaptive with respect to the unknown number of contaminations. The optimal convergence rates ...
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作者：He, Yinqiu; Xu, Gongjun; Wu, Chong; Pan, Wei
作者单位：University of Michigan System; University of Michigan; State University System of Florida; Florida State University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the l(p)-norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed. Moreover, they are also as...
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作者：Hamm, Thomas; Steinwart, Ingo
作者单位：University of Stuttgart
摘要：We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under some standard regularity assumptions for regression and classification, we prove learning rates, in which the dimension of the ambient space is replaced by the box-counting dimension of the support of the data generating distribution. In the regression case...
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作者：Chakraborty, Moumita; Ghosal, Subhashis
作者单位：North Carolina State University
摘要：For nonparametric univariate regression under a monotonicity constraint on the regression function f, we study the coverage of a Bayesian credible interval for f (x(0)), where x(0) is an interior point. Analysis of the posterior becomes a lot more tractable by considering a projection-posterior distribution based on a finite random series of step functions with normal basis coefficients as a prior for f. A sample f from the resulting conjugate posterior distribution is projected on the space o...
