TY - JOUR
T1 - Optimal subsampling algorithms for composite quantile regression in massive data
AU - Jin, Jun
AU - Liu, Shuangzhe
AU - Ma, Tiefeng
N1 - Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023/7/24
Y1 - 2023/7/24
N2 - Massive datasets have gained increasing prominence across various fields, but their analysis is often impeded by computational limitations. In response, Wang and Ma (Optimal subsampling for quantile regression in big data. Biometrika. 2021;108:99–112) have proposed an optimal subsampling method for quantile regression in massive datasets. Composite quantile regression, as a robust and efficient alternative to ordinary least squares regression and quantile regression in linear models, presents further complexities due to its distinct loss function. This paper extends the optimal subsampling method to accommodate composite quantile regression problems. We begin by deriving two new optimal subsampling probabilities for composite quantile regression, considering both the L- and A-optimality criteria Subsequently, we develop an adaptive two-step method based on these probabilities. The resulting estimators exhibit desirable asymptotic properties. In addition, to estimate the variance-covariance matrix without explicitly estimating the densities of the responses, we propose a combining subsamples method. Numerical studies on simulated and real data are conducted to assess and showcase the practical performance of our proposed methods.
AB - Massive datasets have gained increasing prominence across various fields, but their analysis is often impeded by computational limitations. In response, Wang and Ma (Optimal subsampling for quantile regression in big data. Biometrika. 2021;108:99–112) have proposed an optimal subsampling method for quantile regression in massive datasets. Composite quantile regression, as a robust and efficient alternative to ordinary least squares regression and quantile regression in linear models, presents further complexities due to its distinct loss function. This paper extends the optimal subsampling method to accommodate composite quantile regression problems. We begin by deriving two new optimal subsampling probabilities for composite quantile regression, considering both the L- and A-optimality criteria Subsequently, we develop an adaptive two-step method based on these probabilities. The resulting estimators exhibit desirable asymptotic properties. In addition, to estimate the variance-covariance matrix without explicitly estimating the densities of the responses, we propose a combining subsamples method. Numerical studies on simulated and real data are conducted to assess and showcase the practical performance of our proposed methods.
KW - asymptotic distribution
KW - combining subsamples
KW - Composite Quantile regression
KW - massive data
KW - optimal subsampling
UR - http://www.scopus.com/inward/record.url?scp=85165672279&partnerID=8YFLogxK
U2 - 10.1080/02331888.2023.2239507
DO - 10.1080/02331888.2023.2239507
M3 - Article
AN - SCOPUS:85165672279
SN - 0233-1888
VL - 57
SP - 811
EP - 843
JO - Statistics
JF - Statistics
IS - 4
ER -