Optimal subsampling for quantile regression in big data

Summary We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the asymptotic variance-covariance matrix for a linearly...

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Bibliographic Details
Published in:Biometrika 2021-03, Vol.108 (1), p.99-112
Main Authors: Wang, Haiying, Ma, Yanyuan
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Computer applications
Covariance matrix
Estimators
Iterative methods
Optimization
Parameter estimation
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Summary:Summary We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator and the other minimizes that of the original parameter estimator. The former does not depend on the densities of the responses given covariates and is easy to implement. Algorithms based on optimal subsampling probabilities are proposed and asymptotic distributions, and the asymptotic optimality of the resulting estimators are established. Furthermore, we propose an iterative subsampling procedure based on the optimal subsampling probabilities in the linearly transformed parameter estimation which has great scalability to utilize available computational resources. In addition, this procedure yields standard errors for parameter estimators without estimating the densities of the responses given the covariates. We provide numerical examples based on both simulated and real data to illustrate the proposed method.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asaa043