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作者：Duffy, James A.; Kasparis, Ioannis
作者单位：University of Oxford; University of Cyprus
摘要：We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity-what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d = 1/2, and arrays of autoregressive processes with roots drifting slowly towards unity. We first apply the theory to study inference in parametric and nonparametric regression models involving WNPs as covariates. We then use these results to d...
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作者：Hallin, Marc; Del Barrio, Eustasio; Cuesta-Albertos, Juan; Matran, Carlos
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Universidad de Valladolid; Universidad de Valladolid; Universidad de Cantabria
摘要：Unlike the real line, the real space R-d, for d >= 2, is not canonically ordered. As a consequence, such fundamental univariate concepts as quantile and distribution functions and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has been an open problem for more than half a century, generating an abundant literature and motivating, among others, the development of statistical depth and c...
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作者：Zou, Nan; Volgushev, Stanislav; Buecher, Axel
作者单位：University of Toronto; Heinrich Heine University Dusseldorf
摘要：Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from different blocks are dependent. Theory respecting the latter complications is not well developed, and, in the multivariate case, has only recently bee...
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作者：Gerber, Mathieu; Heine, Kari
作者单位：University of Bristol; University of Bath
摘要：Let (Y-t)(t >= 1) be a sequence of i.i.d. observations and {f(theta), theta is an element of R-d} be a parametric model. We introduce a new online algorithm for computing a sequence ((theta) over cap (t))(t >= 1), which is shown to converge almost surely to argmax(theta is an element of Rd) E[log f(theta)(Y-1)] at rate O(log(t)((1+epsilon)/2t-1/2)), with epsilon > 0 a user specified parameter. This convergence result is obtained under standard conditions on the statistical model and, most nota...
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作者：Jin, Jiashun; Ke, Zheng Tracy; Luo, Shengming
作者单位：Carnegie Mellon University; Harvard University
摘要：Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed memberships, (c) have a tractable null distribution and (d) adapt automatically to different levels of sparsity, and achieve the optimal phase diagram. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fixing m >= 3, for each m-g...
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作者：Lin, Zhantao; Flournoy, Nancy; Rosenberger, William F.
作者单位：George Mason University; University of Missouri System; University of Missouri Columbia
摘要：Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients' biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture of normal distribut...
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作者：Loeffler, Matthias; Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Pennsylvania; Yale University
摘要：Spectral clustering is one of the most popular algorithms to group high-dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian mixture model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are...
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作者：Pang, Shanqi; Wang, Jing; Lin, Dennis K. J.; Liu, Min-Qian
作者单位：Henan Normal University; Shanghai Normal University; Purdue University System; Purdue University; Nankai University; Nankai University
摘要：A considerable portion of the work on mixed orthogonal arrays applies specifically to arrays of strength 2. Although strength t = 2 is arguably the most important case for statistical applications, there is an urgent need for better methods for t >= 3. However, the knowledge on the existence of arrays for t >= 3 is rather limited. In this paper, new construction methods for symmetric and asymmetric orthogonal arrays (OAs) with high strength are proposed by using lower strength orthogonal parti...
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作者：Lee, Sokbae; Liao, Yuan; Seo, Myung Hwan; Shin, Youngki
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick; Seoul National University (SNU); McMaster University
摘要：We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero...
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作者：Bercu, Bernard; Bigot, Jeremie
作者单位：Universite de Bordeaux; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is devoted to the stochastic approximation of entropically regularized-Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal transportation problems can be rewritten as a nonstrongly concave optimisation problem. It allows to implement a Robbins-Monro stochastic algorithm to estimate the Sinkhorn divergence using a sequence of data sampled from one of the two distributions. Our main contribut...
