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作者：Kirchner, Kristin; Bolin, David
作者单位：Delft University of Technology; King Abdullah University of Science & Technology
摘要：Optimal linear prediction (aka. kriging) of a random field {Z(x)}(x is an element of X )indexed by a compact metric space (X, d(X)) can be obtained if the mean value function m : chi -> R and the covariance function Q: X x X -> R of Z are known. We consider the problem of predicting the value of Z (x*) at some location x* is an element of X based on observations at locations {x(j)}(j=1)(n), which accumulate at x* as n -> infinity (or, more generally, predicting phi(Z) based on {phi(j)(Z)}(j=i)...
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作者：Dalalyan, Arnak S.; Minasyan, Arshak
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Yerevan State University
摘要：The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time, which is at most polynomial in dimension, sample size and the logarithm of the inverse of the contamination rate. Second, it is equivariant by translations, uniform scaling and orthogonal transformations. Third, it has a high breakdown point equal to 0.5, a...
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作者：Lee, Kuang-Yao; Li, Lexin
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of California System; University of California Berkeley
摘要：Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Frechet der...
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作者：Zhao, Anqi; Ding, Peng
作者单位：National University of Singapore; University of California System; University of California Berkeley
摘要：The split-plot design arose from agricultural science with experimental units, also known as the subplots, nested within groups known as the whole plots. It assigns different interventions at the whole-plot and subplot levels, respectively, providing a convenient way to accommodate hard-to-change factors. By design, subplots within the same whole plot receive the same level of the whole-plot intervention, and thereby induce a group structure on the final treatment assignments. A common strateg...
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作者：Gao, Lan; Shao, Qi-Man; Shi, Jiasheng
作者单位：Chinese University of Hong Kong; Southern University of Science & Technology; University of Southern California; University of Pennsylvania
摘要：Let {(Xi, Yi)}(i=1)(n) be a sequence of independent bivariate random vec- tors. In this paper, we establish a refined Cramer-type moderate deviation theorem for the general self-normalized sum Sigma(n)(i=1) X-i/(Sigma(n)(i=1) Y-i(2))(1/2), which unifies and extends the classical Cramer (Actual. Sci. Ind. 736 (1938) 5-23) theorem and the self-normalized Cramer-type moderate deviation theorems by Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167-2215) as well as the further refined version by Wan...
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作者：Hastie, Trevor; Montanari, Andrea; Rosset, Saharon; Tibshirani, Ryan J.
作者单位：Stanford University; Stanford University; Stanford University; Tel Aviv University; Carnegie Mellon University; Carnegie Mellon University
摘要：Interpolators-estimators that achieve zero training error-have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum l(2) norm (ridgeless) interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature distribution: a linear model...
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作者：Bing, Xin; Ning, Yang; Xu, Yaosheng
作者单位：Cornell University
摘要：A prominent concern of scientific investigators is the presence of unobserved hidden variables in association analysis. Ignoring hidden variables often yields biased statistical results and misleading scientific conclusions. Motivated by this practical issue, this paper studies the multivariate response regression with hidden variables, Y = (psi*)(T) X + (B*)(T) Z + E, where Y is an element of R-m is the response vector, X is an element of R-p is the observable feature, Z is an element of R-K ...
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作者：Cai, T. Tony; Wei, Hongji
作者单位：University of Pennsylvania
摘要：Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov class, which serves as a benchmark for the cost of adaptation, is established. We then quantify the exact communication cost for adaptation and construct an optimally adaptive procedure for distributed estimation over a range of Besov classes. The results de...
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作者：Gamarnik, David; Zadik, Ilias
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We consider a sparse high-dimensional regression model where the goal is to recover a k-sparse unknown binary vector beta* from n noisy linear observations of the form Y = X beta* + W is an element of R-n where X is an element of R-n has i.i.d. N(0, 1) entries and W is an element of R-n has i.i.d. N(0, sigma(2)) entries. In the high signal-to-noise ratio regime and sublinear sparsity regime, while the order of the sample size needed to recover the unknown vector information-theoretically is kn...
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作者：Xia, Dong; Zhang, Anru R.; Zhou, Yuchen
作者单位：Hong Kong University of Science & Technology; Duke University; Duke University; Duke University; University of Pennsylvania
摘要：In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the data-driven confidence regions for the singular subspace of the parameter tensor based on the asymptotic distribution of an updated estimate by two-iteration alternating minimization. The asymptotic distributions are established under some essential condition...
