Optimal subsampling for composite quantile regression in big data

Xiaohui Yuan (), Yong Li (), Xiaogang Dong () and Tianqing Liu
Additional contact information
Xiaohui Yuan: Jilin University
Yong Li: Jilin University
Xiaogang Dong: Changchun University of Technology
Tianqing Liu: Jilin University

Statistical Papers, 2022, vol. 63, issue 5, No 12, 1649-1676

Abstract: Abstract The composite quantile regression (CQR) is an efficient and robust alternative to the least squares for estimating regression coefficients in a linear model. We investigate optimal subsampling for CQR with massive datasets. By establishing the consistency and asymptotic normality of the CQR estimator from a general subsampling algorithm, we derive the optimal subsampling probabilities under the L- and A-optimality criteria. The L-optimality criterion minimizes the trace of the asymptotic variance–covariance matrix of the estimator for a linearly transformed regression parameters and the A-optimality criterion minimizes that of the estimator for regression parameters. The L-optimal subsampling probabilities is easy to implement as they do not depend on the densities of the responses given covariates. Based on the L-optimal subsampling probabilities, we propose algorithms for computing the resulting estimators and their asymptotic distributions and asymptotic optimality are established. To obtain standard errors for CQR estimators without estimating the densities of the responses given the covariates, we propose an iterative subsampling procedure based on the L-optimal subsampling probabilities. The proposed methods are illustrated through numerical experiments on simulated and real datasets.

Keywords: Asymptotic distribution; Composite quantile regression; Massive data; L-optimality; Optimal subsampling (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00362-022-01292-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-022-01292-1

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-022-01292-1

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().