Local expectations of the population spectral distribution of a high-dimensional covariance matrix

Weiming Li ()

Statistical Papers, 2014, vol. 55, issue 2, 563-573

Abstract: This paper discusses the relationship between the population spectral distribution and the limit of the empirical spectral distribution in high-dimensional situations. When the support of the limiting spectral distribution is split into several intervals, the population one gains a meaningful division, and general functional expectations of each part from the division, referred as local expectations, can be formulated as contour integrals around these intervals. Basing on these knowledge we present consistent estimators of the local expectations and prove a central limit theorem for them. The results are then used to analyze an estimator of the population spectral distribution in recent literature. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: High-dimensional covariance matrix; Limiting spectral distribution; Local expectation; Population spectral distribution; Stieltjes transform (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-013-0501-6 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:55:y:2014:i:2:p:563-573

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-013-0501-6

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().