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Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics
Publikationstyp
Journal Article
Date Issued
2012-05-28
Sprache
English
Author(s)
Volume
56
Issue
1
Start Page
1
End Page
20
Citation
Theory of Probability and its Applications 56 (1): 1-20 (2012-05-28)
Publisher DOI
Scopus ID
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix A, which is invertible as a bounded operator on ℓ 2, can be uniformly approximated by banded matrices, then so can the inverse of A. We give explicit formulas for the banded approximations of A -1 as well as bounds on their accuracy and speed of convergence in terms of their bandwidth. We then use these results to prove that the so-called Wiener algebra is inverse closed. In the second part of the paper we apply these results to covariance matrices ∑ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of ∑. Finally, we note some applications of our results to statistics. © by SIAM.
Subjects
Gaussian stochastic processes
High dimensional statistical inference
Infinite band-dominated matrices
Mixing conditions
DDC Class
510: Mathematik