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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...
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作者：Bandypadhyay, Soutir; Lahiri, Soumendra N.; Nordman, Daniel J.
作者单位：Lehigh University; North Carolina State University; Iowa State University
摘要：This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FUEL) methodology for time series (on a regular grid), the formulation of the spatial I-DEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures. A spat...
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作者：Cheng, Ching-Shui; Kao, Ming-Hung
作者单位：Academia Sinica - Taiwan; University of California System; University of California Berkeley; Arizona State University; Arizona State University-Tempe
摘要：Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the mental stimulus, and ...
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作者：Chen, Yen-Chi; Genovese, Christopher R.; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：The large sample theory of estimators for density modes is well understood. In this paper we consider density ridges, which are a higher-dimensional extension of modes. Modes correspond to zero-dimensional, local high-density regions in point clouds. Density ridges correspond to s-dimensional, local high-density regions in point clouds. We establish three main results. First we show that under appropriate regularity conditions, the local variation of the estimated ridge can be approximated by ...
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作者：Jentsch, Carsten; Plitis, Dimitris N.
作者单位：University of Mannheim; University of California System; University of California San Diego
摘要：Multivariate time series present many challenges, especially when they are high dimensional. The paper's focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices that we conveniently stack into one huge matrix. We are then able to show consistency of an estimator based on the so-called flat-top tapers; most importantly, the consistency holds true even when the time series dimension is allowed to increase with the sam...
