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作者：Aston, John A. D.; Pigoli, Davide; Tavakoli, Shahin
作者单位：University of Cambridge
摘要：The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons, or due to a small sample size. However, inferential tools to verify this assumption are somewhat lacking in high-dimensional or functional data analysis settings, where this assumption is most relevant. We propose here to tes...
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作者：Cai, T. Tony; Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Pennsylvania
摘要：We study in this paper computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple nonoverlapping) signal submatrix (of magnitude. and size k(m) x k(n)) embedded in a large noise matrix (of size mxn), the goal is to optimal identify the support of the signal submatrix computationally and statistically. Two transition thresholds for the signal-to-noise ratio lambda/ sigma are established in terms of m, n, k(m) and k(n). The first threshold, SNR...
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作者：Dette, Holger; Konstantinou, Maria; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of observations and considers the asymptotic properties of estimators and designs as the sample size converges to infinity, our approach is based on a continuous time model. We use results from stochastic analysis to identify the best linear unbiased estimator (BL...
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作者：Zheng, Wei; Ai, Mingyao; Li, Kang
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis; Peking University
摘要：Many applications of block designs exhibit neighbor and edge effects. A popular remedy is to use the circular design coupled with the interference model. The search for optimal or efficient designs has been intensively studied in recent years. The circular neighbor balanced designs at distances 1 and 2 (CNBD2), including orthogonal array of type I (OAI) of strength 2, are the two major designs proposed in literature for the purpose of estimating the direct treatment effects. They are shown to ...
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作者：Jiang, Tiefeng; Leder, Kevin; Xu, Gongjun
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; University of Michigan System; University of Michigan
摘要：In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulat...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：The present paper considers the problem of estimating a linear functional Phi = integral(infinity)(-infinity) phi(x) f (x) dx of an unknown deconvolution density f on the basis of n i. i. d. observations, Y-1,..., Y-n of Y = theta +xi, where xi has a known pdf g, and f is the pdf of theta. The objective of the present paper is to develop the a general minimax theory of estimating Phi, and to relate this problem to estimation of functionals Phi(n) = n(-1) Sigma(n)(i=1) phi(theta(i)) in indirect...
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作者：Bibinger, Markus; Jirak, Moritz; Vetter, Mathias
作者单位：Braunschweig University of Technology; University of Kiel
摘要：In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Ito semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test s...
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作者：Boistard, Helene; Lopuhaa, Hendrik P.; Ruiz-Gazen, Anne
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Delft University of Technology
摘要：For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the Hajek empirical process centered by their finite population mean as well as by their super-population mean in a survey sampling framework. The results apply to single-stage unequal probability sampling designs and essentially only require conditions on higher order correlations. We apply our main results to a Hadamard differentiable statistical f...
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作者：Ernst, Philip A.; Shepp, Larry A.; Wyner, Abraham J.
作者单位：Rice University; University of Pennsylvania
摘要：In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically prove Yule's 1926 empirical finding of nonsense correlation [J. Roy. Statist. Soc. 89 (1926) 1-63], which we do by analytically determining the second moment of the empirical correlation coefficient theta : = integral(1)(0) W-1(t) W-2(t) dt - integral(1)(0) W-1(t) dt integral(1)(0) W-2(t) dt/root integral(1)(0) W-1(2)(t) dt - (integral(1)(0) W-1(t) dt)(2) root integral(1)(0) W-2(2)(t) dt - (inte...
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作者：Basu, Kinjal; Mukherjee, Rajarshi
作者单位：Stanford University
摘要：In a very recent work, Basu and Owen [Found. Comput. Math. 17 (2017) 467-496] propose the use of scrambled geometric nets in numerical integration when the domain is a product of s arbitrary spaces of dimension d having a certain partitioning constraint. It was shown that for a class of smooth functions, the integral estimate has variance O(n(-1-2/d) (log n)(s-1)) for scrambled geometric nets compared to O(n(-1)) for ordinaryMonte Carlo. The main idea of this paper is to expand on the work by ...
