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作者：Feng, Oliver Y.; Guntuboyina, Adityanand; Kim, Arlene K. H.; Samworth, Richard J.
作者单位：University of Cambridge; University of California System; University of California Berkeley; Korea University
摘要：We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piece-wise affine. The complexity of such densities f can be measured in terms of the sum Gamma(f) of the numbers of facets of the subdomains in the polyhedral subdivision of the support induced by f. Given n independent observations from a d-dimensional log-concave density wi...
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作者：Belitser, Eduard; Ghosal, Subhashis; van Zanten, Harry
作者单位：Vrije Universiteit Amsterdam; North Carolina State University
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作者：Petersen, Alexander; Liu, Xi; Divani, Afshin A.
作者单位：University of California System; University of California Santa Barbara; University of New Mexico
摘要：Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the un- certainty associated with the estimated cond...
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作者：Fissler, Tobias; Ziegel, Johanna F.
作者单位：Vienna University of Economics & Business; University of Bern
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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：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：Shi, Chengchun; Song, Rui; Lu, Wenbin
作者单位：University of London; London School Economics & Political Science; North Carolina State University
摘要：Personalized medicine is a medical procedure that receives considerable scientific and commercial attention. The goal of personalized medicine is to assign the optimal treatment regime for each individual patient, according to his/her personal prognostic information. When there are a large number of pretreatment variables, it is crucial to identify those important variables that are necessary for treatment decision making. In this paper, we study two information criteria: the concordance and v...
