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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：In this paper, the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressi...
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作者：Bhattacharya, Anirban; Pati, Debdeep; Yang, Yun
作者单位：Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback-Leibler (KL) neighborhood of the true parameter (or the KL divergence minimizer in the misspeci...
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作者：De Castro, Yohann; Gamboa, Fabrice; Henrion, Didier; Hesst, Roxana; Lasserre, Jean-Bernard
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semialgebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This article shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy in...
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作者：Kontorovich, Aryeh; Pinelis, Iosif
作者单位：Ben-Gurion University of the Negev; Michigan Technological University
摘要：We provide an exact nonasymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-approximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized voting procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form c(infinity)/root nu as v -> infinity, where c(infinity) = 0.16997... is a universal ...
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作者：Chen, Song Xi; Li, Jun; Zhong, Ping-Shou
作者单位：Peking University; Peking University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Michigan State University
摘要：This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate L-2-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal enhancement. It is shown tha...
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作者：Cook, R. Dennis; Forzani, Liliana
作者单位：University of Minnesota System; University of Minnesota Twin Cities; National University of the Littoral
摘要：We study the asymptotic behavior of predictions from partial least squares (PLS) regression as the sample size and number of predictors diverge in various alignments. We show that there is a range of regression scenarios where PLS predictions have the usual root-n convergence rate, even when the sample size is substantially smaller than the number of predictors, and an even wider range where the rate is slower but may still produce practically useful results. We show also that PLS predictions ...
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作者：Zhang, Anru
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In addition, the implementation of some previous methods are NP-hard. In this article, we propose a framework for low-rank tensor completion via a novel tensor measurement scheme that ...
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作者：Bhattacharjee, Monika; Bose, Arup
作者单位：State University System of Florida; University of Florida; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：Consider a high-dimensional linear time series model where the dimen- sion p and the sample size n grow in such a way that p/n -> 0. Let (Gamma) over cap (u) be the uth order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in {(Gamma) over cap (u) , (Gamma) over cap (u)*, u >= 0} exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, i...
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作者：Shu, Hai; Nan, Bin
作者单位：University of Michigan System; University of Michigan; University of California System; University of California Irvine
摘要：We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that several commonly used methods for independent observations can be applied to the temporally dependent data. In particular, the rates of convergence are obtained for the generalized thr...
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作者：Lian, Heng; Zhao, Kaifeng; Lv, Shaogao
作者单位：City University of Hong Kong; Philips; Philips Research; Nanjing Audit University
摘要：In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to th...
