Abstract
Factor models aim to describe a dependence structure among high-dimensional random variables in terms of a low-dimensional unobserved random vector called a factor. One of the major practical issues of applying the factor model is to determine the factor dimensionality. In this paper, we propose a computationally feasible nonparametric prior distribution which achieves the posterior consistency of the factor dimensionality. We also derive the posterior contraction rate of the covariance matrix which is optimal when the factor dimensionality of the true covariance matrix is bounded. We conduct numerical studies that illustrate our theoretical results.
Funding Statement
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C3A01003550).
Acknowledgments
The authors would like to thank the associate editor and three referees for numerous comments and suggestions that helped considerably improve an earlier version of the paper.
Citation
Ilsang Ohn. Yongdai Kim. "Posterior Consistency of Factor Dimensionality in High-Dimensional Sparse Factor Models." Bayesian Anal. 17 (2) 491 - 514, June 2022. https://doi.org/10.1214/21-BA1261
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