Factorized estimation of high‐dimensional nonparametric covariance models

Jian Zhang and Jie Li

Scandinavian Journal of Statistics, 2022, vol. 49, issue 2, 542-567

Abstract: Estimation of covariate‐dependent conditional covariance matrix in a high‐dimensional space poses a challenge to contemporary statistical research. The existing kernel estimators may not be locally adaptive due to using a single bandwidth to explore the smoothness of all entries of the target matrix function. In this paper, we propose a novel framework to address this issue, where we factorize the target matrix into factors and estimate these factors in turn by the kernel approach. The resulting estimator is further regularized by thresholding and optimal shrinkage. Under certain mixing and sparsity conditions, we show that the proposed estimator is well‐conditioned and uniformly consistent with the underlying matrix function even when the sample is dependent. Simulation studies suggest that the proposed estimator significantly outperforms its competitors in terms of integrated root‐squared estimation error. We present an application to financial return data.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/sjos.12529

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:bla:scjsta:v:49:y:2022:i:2:p:542-567

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().