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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...
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作者：Albert, Melisande; Bouret, Yann; Fromont, Magalie; Reynaud-Bouret, Patricia
作者单位：Universite Cote d'Azur; Universite Cote d'Azur; Universite Rennes 2; Universite de Rennes
摘要：Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are resealed general U-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap ...
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作者：Fan, Jianqing; Rigollet, Philippe; Wang, Weichen
作者单位：Princeton University; Massachusetts Institute of Technology (MIT)
摘要：High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other l(r) norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are spar...
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作者：Gao, Chao; Zhou, Harrison H.
作者单位：Yale University
摘要：Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA were established under various interesting settings. On the other side, Bayesian methods are becoming...
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作者：Einmahl, John H. J.; Li, Jun; Lui, Regina Y.
作者单位：Tilburg University; University of California System; University of California Riverside; Rutgers University System; Rutgers University New Brunswick
摘要：Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical half-space depth usel...
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作者：Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong
作者单位：Stanford University; Harvard University; Harvard University
摘要：In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a functio...
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作者：Tuo, Rui; Wu, C. F. Jeff
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University System of Georgia; Georgia Institute of Technology
摘要：Many computer models contain unknown parameters which need to be estimated using physical observations. Tuo and Wu (2014) show that the calibration method based on Gaussian process models proposed by Kennedy and O'Hagan [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 425-464] may lead to an unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L-2 calibration, and...
