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. INDEX TERMS CSL function, expectile regression, large-scale data, missing at random, proximal ADMM algorithm.

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