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作者：Comte, Fabienne; Johannes, Jan
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Catholique Louvain
摘要：We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows us to cover the prediction problem with respect to the mean squared prediction error as well as the estimation of the slope function and it...
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作者：Cai, T. Tony; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax lower bound. The problem exhibits new features that are significantly different from those that occur in the conventional nonparametric function estimation problems. Standard techniques fail to yield good results, and new tools are thus needed. We first develo...
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作者：Zhu, Hongtu; Li, Runze; Kong, Linglong
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Alberta
摘要：Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then...
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作者：Dalalyan, Arnak S.; Salmon, Joseph
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Cite
摘要：We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in nonparametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression, kernel ridge regression, shrinking estimato...
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作者：Qiu, Yumou; Chen, Song Xi
作者单位：Iowa State University; Peking University; Peking University
摘要：Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Sigma, we propose a test for Sigma being banded with possible diverging bandwidth. The test is adaptive to the large p, small n situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator are investigated by theoretical ...
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作者：Li, Jun; Chen, Song Xi
作者单位：Iowa State University; Peking University; Peking University
摘要：We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the large p, small n situations and (ii) without assuming parametric distributions for the ...
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作者：Chen, Dong; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which ...
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作者：Cisewski, Jessi; Hannig, Jan
作者单位：Carnegie Mellon University; University of North Carolina; University of North Carolina Chapel Hill
摘要：While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval...
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作者：Su, Yu-Ru; Wang, Jane-Ling
作者单位：University of California System; University of California Davis; National Cheng Kung University; University of California System; University of California Davis
摘要：There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open...
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作者：Tang, Yu; Xu, Hongquan; Lin, Dennis K. J.
作者单位：Soochow University - China; University of California System; University of California Los Angeles; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method ...
