Singular vector distribution of sample covariance matrices
dc.contributor.author | Ding, Xiucai | |
dc.date.accessioned | 2019-11-21T19:41:53Z | |
dc.date.available | 2019-11-21T19:41:53Z | |
dc.date.issued | 2019-03 | |
dc.date.updated | 2019-11-21T19:41:52Z | |
dc.description.abstract | <jats:title>Abstract</jats:title><jats:p>We consider a class of sample covariance matrices of the form <jats:italic>Q</jats:italic> = <jats:italic>TXX</jats:italic><jats:italic>T</jats:italic>, where <jats:italic>X</jats:italic> = (<jats:italic>x</jats:italic><jats:sub><jats:italic>ij</jats:italic></jats:sub>) is an <jats:italic>M</jats:italic>×<jats:italic>N</jats:italic> rectangular matrix consisting of independent and identically distributed entries, and <jats:italic>T</jats:italic> is a deterministic matrix such that <jats:italic>T</jats:italic>*<jats:italic>T</jats:italic> is diagonal. Assuming that <jats:italic>M</jats:italic> is comparable to <jats:italic>N</jats:italic>, we prove that the distribution of the components of the right singular vectors close to the edge singular values agrees with that of Gaussian ensembles provided the first two moments of <jats:italic>x</jats:italic><jats:sub><jats:italic>ij</jats:italic></jats:sub> coincide with the Gaussian random variables. For the right singular vectors associated with the bulk singular values, the same conclusion holds if the first four moments of <jats:italic>x</jats:italic><jats:sub><jats:italic>ij</jats:italic></jats:sub> match those of the Gaussian random variables. Similar results hold for the left singular vectors if we further assume that <jats:italic>T</jats:italic> is diagonal.</jats:p> | |
dc.identifier.issn | 0001-8678 | |
dc.identifier.issn | 1475-6064 | |
dc.identifier.uri | ||
dc.language | en | |
dc.publisher | Cambridge University Press (CUP) | |
dc.relation.ispartof | Advances in Applied Probability | |
dc.relation.isversionof | 10.1017/apr.2019.10 | |
dc.title | Singular vector distribution of sample covariance matrices | |
dc.type | Journal article | |
pubs.begin-page | 236 | |
pubs.end-page | 267 | |
pubs.issue | 01 | |
pubs.organisational-group | Staff | |
pubs.organisational-group | Duke | |
pubs.organisational-group | Mathematics | |
pubs.organisational-group | Trinity College of Arts & Sciences | |
pubs.publication-status | Published | |
pubs.volume | 51 |
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