Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution

Author(s): Han, Fang; Liu, Han

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr13g4q
DC FieldValueLanguage
dc.contributor.authorHan, Fang-
dc.contributor.authorLiu, Han-
dc.date.accessioned2021-10-11T14:17:05Z-
dc.date.available2021-10-11T14:17:05Z-
dc.date.issued2017en_US
dc.identifier.citationHan, Fang, and Liu, Han. "Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution." Bernoulli 23, no. 1 (2017): pp. 23-57. doi:10.3150/15-BEJ702.en_US
dc.identifier.issn1350-7265-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr13g4q-
dc.description.abstractCorrelation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson’s sample correlation matrix. Although Pearson’s sample correlation matrix enjoys various good properties under Gaussian models, it is not an effective estimator when facing heavy-tailed distributions. As a robust alternative, Han and Liu [J. Am. Stat. Assoc. 109 (2015) 275–287] advocated the use of a transformed version of the Kendall’s tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall’s tau sample correlation matrix and its transformed version proposed in Han and Liu [J. Am. Stat. Assoc. 109 (2015) 275–287] for estimating the population Kendall’s tau correlation matrix and the latent Pearson’s correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of “effective rank” in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a “sign sub-Gaussian condition” which is sufficient to guarantee that the rank-based correlation matrix estimator attains the fast rate of convergence. In both cases, we do not need any moment condition.en_US
dc.format.extent23 - 57en_US
dc.language.isoen_USen_US
dc.relation.ispartofBernoullien_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleStatistical analysis of latent generalized correlation matrix estimation in transelliptical distributionen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.3150/15-BEJ702-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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