Weak Convergence of the Empirical Spectral Distribution of High-Dimensional Band Sample Covariance Matrices

Kamil Jurczak ()
Additional contact information
Kamil Jurczak: Ruhr-Universität Bochum

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1273-1302

Abstract: Abstract In this article, we investigate high-dimensional band sample covariance matrices under the regime that the sample size n, the dimension p, and the bandwidth d tend simultaneously to infinity such that $$\begin{aligned} n/p\rightarrow 0 \ \ \text {and} \ \ d/n\rightarrow y>0. \end{aligned}$$ n / p → 0 and d / n → y > 0 . It is shown that the empirical spectral distribution of those matrices converges weakly to a deterministic probability measure with probability 1. The limiting measure is characterized by its moments. Certain restricted compositions of natural numbers play a crucial role in the evaluation of the expected moments of the empirical spectral distribution.

Keywords: High-dimensional sample covariance matrices; Empirical spectral distribution; Strong convergence; Weak convergence; Method of moments; Number of restricted compositions of a natural number; 60B20 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-017-0751-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0751-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-017-0751-7

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().