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September 2020 Bayesian Bandwidth Test and Selection for High-dimensional Banded Precision Matrices
Kyoungjae Lee, Lizhen Lin
Bayesian Anal. 15(3): 737-758 (September 2020). DOI: 10.1214/19-BA1167

Abstract

Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrices. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although there exist some consistent frequentist tests for the bandwidth parameter, bandwidth selection consistency for precision matrices has not been established in a Bayesian framework. In this paper, we propose a prior distribution tailored to the bandwidth estimation of high-dimensional precision matrices. The banded structure is imposed via the Cholesky factor from the modified Cholesky decomposition. We establish strong model selection consistency for the bandwidth as well as consistency of the Bayes factor. The convergence rates for Bayes factors under both the null and alternative hypotheses are derived which yield similar order of rates. As a by-product, we also propose an estimation procedure for the Cholesky factors yielding an almost optimal order of convergence rates. Two-sample bandwidth test is also considered, and it turns out that our method is able to consistently detect the equality of bandwidths between two precision matrices. The simulation study confirms that our method in general outperforms the existing frequentist and Bayesian methods.

Citation

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Kyoungjae Lee. Lizhen Lin. "Bayesian Bandwidth Test and Selection for High-dimensional Banded Precision Matrices." Bayesian Anal. 15 (3) 737 - 758, September 2020. https://doi.org/10.1214/19-BA1167

Information

Published: September 2020
First available in Project Euclid: 19 June 2019

MathSciNet: MR4132648
Digital Object Identifier: 10.1214/19-BA1167

Subjects:
Primary: 62C10, 62H15
Secondary: 62F05

JOURNAL ARTICLE
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Vol.15 • No. 3 • September 2020
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