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作者：Todorov, Viktor
作者单位：Northwestern University
摘要：We derive a nonparametric estimator of the jump-activity index beta of a locally-stable pure-jump Ito semimartingale from discrete observations of the process on a fixed time interval with mesh of the observation grid shrinking to zero. The estimator is based on the empirical characteristic function of the increments of the process scaled by local power variations formed from blocks of increments spanning shrinking time intervals preceding the increments to be scaled. The scaling serves two pu...
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作者：Fougeres, Anne-Laure; de Haan, Laurens; Mercadier, Cecile
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang [Statistics of bivariate extremes (1...
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作者：Dette, Holger; Melas, Viatcheslav B.; Guchenko, Roman
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs...
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作者：Gao, Chao; Ma, Zongming; Ren, Zhao; Zhou, Harrison H.
作者单位：Yale University; University of Pennsylvania; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high-dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high-dimensional applications involving massive data sets. However, there has been few theoreti...
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作者：Jiang, Ci-Ren; Wang, Jane-Ling
作者单位：Academia Sinica - Taiwan; University of California System; University of California Davis
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作者：Ghosal, Subhashis
作者单位：North Carolina State University
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作者：Chan, Hock Peng; Walther, Guenther
作者单位：National University of Singapore; Stanford University
摘要：We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the sparseness of the signa...
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作者：Cai, T. Tony; Li, Xiaodong
作者单位：University of Pennsylvania
摘要：Community detection, which aims to cluster N nodes in a given graph into r distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM) is extended to the generalized stochastic block model (GSBM) that allows for adversarial outlier nodes, which are connected with the other nodes in the graph in an arbitrary way. Under this model, we introduce a procedure using convex optimization followed by k...
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作者：Cheng, Guang; Shang, Zuofeng
作者单位：Purdue University System; Purdue University
摘要：We consider a joint asymptotic framework for studying semi-nonparametric regression models where (finite-dimensional) Euclidean parameters and (infinite-dimensional) functional parameters are both of interest. The class of models in consideration share a partially linear structure and are estimated in two general contexts: (i) quasi-likelihood and (ii) true likelihood. We first show that the Euclidean estimator and (pointwise) functional estimator, which are re-scaled at different rates, joint...
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作者：Krauthgamer, Robert; Nadler, Boaz; Vilenchik, Dan
作者单位：Weizmann Institute of Science; Ben-Gurion University of the Negev
摘要：Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is under what conditions can such algorithms recover the sparse principal components? We study this question for a single-spike model with an l(0)-sparse eigenvector, in the asymptotic...
