File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: On singular values of data matrices with general independent columns

TitleOn singular values of data matrices with general independent columns
Authors
Keywordseigenvalue distribution
Large data matrix
large sample covariance matrices
matrix-valued autoregressive model
realized covariance matrix
separable covariance matrix
singular value distribution
Issue Date1-Apr-2023
PublisherInstitute of Mathematical Statistics
Citation
Annals of Statistics, 2023, v. 51, n. 2, p. 624-645 How to Cite?
AbstractWe analyze the singular values of a large p × n data matrix Xn = (xn1,...,xnn), where the columns {xnj} are independent p-dimensional vectors, possibly with different distributions. Assuming that the covariance matrices Σnj = Cov(xnj) of the column vectors can be asymptotically simultaneously diagonalized, with appropriately converging spectra, we establish a limiting spectral distribution (LSD) for the singular values of Xn when both dimensions p and n grow to infinity in comparable magnitudes. Our matrix model goes beyond and includes many different types of sample covariance matrices in existing work, such as weighted sample covariance matrices, Gram matrices, and sample covariance matrices of a linear time series model. Furthermore, three applications of our general approach are developed. First, we obtain the existence and uniqueness of the LSD for realized covariance matrices of a multi-dimensional diffusion process with anisotropic time-varying co-volatility. Second, we derive the LSD for singular values of data matrices from a recent matrix-valued auto-regressive model. Finally, we also obtain the LSD for singular values of data matrices from a generalized finite mixture model.
Persistent Identifierhttp://hdl.handle.net/10722/342100
ISSN
2023 Impact Factor: 3.2
2023 SCImago Journal Rankings: 5.335
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorMei, T-
dc.contributor.authorWang, C-
dc.contributor.authorYao, J-
dc.date.accessioned2024-04-02T08:25:34Z-
dc.date.available2024-04-02T08:25:34Z-
dc.date.issued2023-04-01-
dc.identifier.citationAnnals of Statistics, 2023, v. 51, n. 2, p. 624-645-
dc.identifier.issn0090-5364-
dc.identifier.urihttp://hdl.handle.net/10722/342100-
dc.description.abstractWe analyze the singular values of a large p × n data matrix Xn = (xn1,...,xnn), where the columns {xnj} are independent p-dimensional vectors, possibly with different distributions. Assuming that the covariance matrices Σnj = Cov(xnj) of the column vectors can be asymptotically simultaneously diagonalized, with appropriately converging spectra, we establish a limiting spectral distribution (LSD) for the singular values of Xn when both dimensions p and n grow to infinity in comparable magnitudes. Our matrix model goes beyond and includes many different types of sample covariance matrices in existing work, such as weighted sample covariance matrices, Gram matrices, and sample covariance matrices of a linear time series model. Furthermore, three applications of our general approach are developed. First, we obtain the existence and uniqueness of the LSD for realized covariance matrices of a multi-dimensional diffusion process with anisotropic time-varying co-volatility. Second, we derive the LSD for singular values of data matrices from a recent matrix-valued auto-regressive model. Finally, we also obtain the LSD for singular values of data matrices from a generalized finite mixture model.-
dc.languageeng-
dc.publisherInstitute of Mathematical Statistics-
dc.relation.ispartofAnnals of Statistics-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjecteigenvalue distribution-
dc.subjectLarge data matrix-
dc.subjectlarge sample covariance matrices-
dc.subjectmatrix-valued autoregressive model-
dc.subjectrealized covariance matrix-
dc.subjectseparable covariance matrix-
dc.subjectsingular value distribution-
dc.titleOn singular values of data matrices with general independent columns-
dc.typeArticle-
dc.identifier.doi10.1214/23-AOS2263-
dc.identifier.scopuseid_2-s2.0-85163944272-
dc.identifier.volume51-
dc.identifier.issue2-
dc.identifier.spage624-
dc.identifier.epage645-
dc.identifier.isiWOS:001022538200009-
dc.identifier.issnl0090-5364-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats