Large-Scale Expectile Regression With Covariates Missing at Random

• Published in: IEEE access Vol. 8; pp. 36502 - 36513
• Main Authors: Pan, Yingli, Liu, Zhan, Cai, Wen
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Convex functions; CSL function; Data models; Data transfer; Distributed databases; Estimation; expectile regression; Inference algorithms; large-scale data; missing at random; Missing data; Normality; Optimization; Parameter estimation; proximal ADMM algorithm; Regression analysis; Regression models; Risk analysis; Statistical analysis
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.2970741

Analysis of large volumes of data is very complex due to not only a high level of skewness and heteroscedasticity of variance but also the phenomenon of missing data. Expectile regression is a popular alternative method of analyzing heterogeneous data. In this paper, we consider fitting a linear expectile regression model for estimating conditional expectiles based on a large quantity of data with covariates missing at random. We construct a communication-efficient surrogate loss (CSL) function to estimate model parameters. The asymptotic normality of the proposed estimator is established. A proximal alternating direction method of multipliers (ADMM) algorithm is developed for distributed statistical optimization on a large quantity of data. Simulation studies are performed to assess the finite-sample performance of the proposed method. Survey data from the Behavioral Risk Factor Surveillance System (BRFSS) is used to demonstrate the utility of the proposed method in practice.