Sparse factor models of high dimension
Statistics Theory
2025-01-23 v2 Statistics Theory
Abstract
We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading matrix accommodate a wide range of sparsity patterns. We prove the sparsistency property of the penalized estimator when the number of parameters is diverging, that is the consistency of the estimator and the recovery of the true zeros entries. These theoretical results are illustrated by finite-sample simulation experiments, and the relevance of the proposed method is assessed by applications to portfolio allocation and macroeconomic data prediction.
Cite
@article{arxiv.2307.05952,
title = {Sparse factor models of high dimension},
author = {Benjamin Poignard and Yoshikazu Terada},
journal= {arXiv preprint arXiv:2307.05952},
year = {2025}
}