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作者：Bao, Zhigang; Ding, Xiucai; Wang, Jingming; Wang, Ke
作者单位：Hong Kong University of Science & Technology; University of California System; University of California Davis
摘要：In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high-dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. In particular, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, that is, the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample size are comparabl...
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作者：Wang, Runmin; Zhu, Changbo; Volgushev, Stanislav; Shao, Xiaofeng
作者单位：Southern Methodist University; University of California System; University of California Davis; University of Toronto; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on U-statistic in Chen and Qin (Ann. Statist. 38 (2010) 808-835) and utilizes the self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 343-366; Shao and Zhang J. Amer. Statist. Assoc. 105 (2010) 1228-1240). Our test targets dense alternatives in the...
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作者：Albert, Melisande; Laurent, Beatrice; Marrel, Amandine; Meynaoui, Anouar
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CEA; Centre National de la Recherche Scientifique (CNRS)
摘要：The Hilbert-Schmidt Independence Criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces that is widely used to test independence between two random vectors. Remains the delicate choice of the kernel. In this work, we develop a new HSIC-based aggregated procedure which avoids such a kernel choice, and provide theoretical guarantees for this procedure. To achieve this, on the one hand, we introduce non-asymptotic single tests based on Gaussian kernels with a given ba...
